pipeline_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This file is to calculate the confidence interval of the 4 moments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "Kko9bjxZNV5j"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import powerlaw\n",
    "import psycopg2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "PCXGzypcNV5v"
   },
   "outputs": [],
   "source": [
    "def fitDist(distributions,data):\n",
    "    df_fit = pd.DataFrame(columns=['dist','parms','loglik']) # dataframe to hold fitting results\n",
    "    # fit distributions\n",
    "    for dist in distributions:\n",
    "        print(dist)\n",
    "        parms = dist.fit(data)\n",
    "        loglik = dist.nnlf(parms,data)\n",
    "        # add fitting results to the dataframe\n",
    "        result = pd.DataFrame([dist.name,parms,loglik]).T\n",
    "        result.columns = df_fit.columns\n",
    "        df_fit = pd.concat([df_fit,result],ignore_index=True)\n",
    "    return df_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "ntv8zlLoNV51"
   },
   "outputs": [],
   "source": [
    "distributions_to_test=[stats.expon,stats.norm,stats.logistic,stats.t,stats.chi2,\n",
    "                 stats.dweibull,stats.beta,stats.lognorm,stats.gamma,stats.skewnorm,stats.f,stats.powerlaw,stats.pareto]\n",
    "def pipeline_(data,distribution=distributions_to_test,Bootstrap=True,tail_analysis=True):\n",
    "    if Bootstrap:\n",
    "        iteration = 5000\n",
    "\n",
    "        len_=len(data)\n",
    "        mean=[]\n",
    "        var=[]\n",
    "        skew=[]\n",
    "        kurto=[]\n",
    "\n",
    "        for i in range( iteration ):\n",
    "            samp=np.random.choice(data,len_,replace=True)\n",
    "            mean.append(np.mean(samp))\n",
    "            var.append(np.var(samp))\n",
    "            skew.append(stats.skew(samp))\n",
    "            kurto.append(stats.kurtosis(samp))\n",
    "        figure,[a,b,c,d]=plt.subplots(1, 4,figsize=(15,5))\n",
    "        a.hist(mean,1000,label='mean')\n",
    "        a.set_xlabel(\"mean\")\n",
    "        b.hist(var,1000,label='variance',color='r')\n",
    "        b.set_xlabel(\"variance\")\n",
    "        c.hist(skew,1000,label='skew',color='y')\n",
    "        c.set_xlabel(\"skew\")\n",
    "        d.hist(kurto,1000,label='kurtosis',color='g')\n",
    "        d.set_xlabel(\"kurtosis\")\n",
    "        plt.show()\n",
    "        print(\"confidence interval for the mean:[%6.4f - %6.4f]\" % (np.percentile(mean,2.5),np.percentile(mean,97.5)))\n",
    "        print(\"confidence interval for the variance:[%6.4f - %6.4f]\" % (np.percentile(var,2.5),np.percentile(var,97.5)))\n",
    "        print(\"confidence interval for the skew:[%6.4f - %6.4f]\" % (np.percentile(skew,2.5),np.percentile(skew,97.5)))\n",
    "        print(\"confidence interval for the kurtosis:[%6.4f - %6.4f]\" % (np.percentile(kurto,2.5),np.percentile(kurto,97.5)))\n",
    "       \n",
    "    if tail_analysis:\n",
    "        x=np.asarray(range(1,len(data)+1))\n",
    "        f=lambda x:1-x/(len(data)+1)\n",
    "        plt.loglog(np.sort(data),f(x),\"x\")\n",
    "        np.seterr(divide='ignore', invalid='ignore')\n",
    "        fit = powerlaw.Fit(data)\n",
    "        tail_split,alpha=fit.xmin,fit.power_law.alpha\n",
    "        print(\"Tail split at {}, alpha_value = {}\".format(tail_split,alpha))\n",
    "        tail=data[data>tail_split]\n",
    "        body=data[data<data]\n",
    "        x_=np.asarray(range(1,len(tail)+1))\n",
    "        f=lambda x:1-x/(len(tail)+1)\n",
    "        Fit=fit.power_law.plot_ccdf(color='r', linewidth=2,label=\"tail_fit\")\n",
    "        Fit.loglog(np.sort(tail),f(x_),'x',label=\"tail_data\")\n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "        res=fitDist(distribution,data)\n",
    "        #true_=res.sort_values(by='loglik',ascending=True).loc[0]\n",
    "        \n",
    "        #print(\"best dist is {}, with parameter {} \".format(true_.dist,true_.parms))\n",
    "        return res,fit\n",
    "\n",
    "        \n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "6-kOoNoYNV56"
   },
   "outputs": [],
   "source": [
    "#this part is to use Juhao's data. If use mine, do not run this code...\n",
    "cleaned_data=pd.read_csv(\"cleaned_data.csv\") # cleaned data based on junhao_CSGO + time spent playing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Connect to database and select csgo.profiles\n",
    "conn = psycopg2.connect(\"dbname='dreamteam' user='weisihan' host='localhost' port='5432' password='weisi9527sj'\")\n",
    "cur = conn.cursor()\n",
    "# load csgo.profiles\n",
    "cur.execute('SELECT * FROM csgo.profiles')\n",
    "colnames = [desc[0] for desc in cur.description]\n",
    "csgo_profiles = cur.fetchall()\n",
    "cur.close()\n",
    "conn.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data shape: (84393, 17)\n",
      "No. of users: 84393\n",
      "\n",
      "There are 17 columns:\n",
      "['user_id', 'nickname', 'total_kills', 'total_deaths', 'total_time_played', 'total_kills_headshot', 'total_shots_hit', 'total_mvps', 'total_wins', 'total_rounds_played', 'total_shots_fired', 'rank_id', 'goal_id', 'steam_id', 'about', 'updated_at', 'compensation']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>nickname</th>\n",
       "      <th>total_kills</th>\n",
       "      <th>total_deaths</th>\n",
       "      <th>total_time_played</th>\n",
       "      <th>total_kills_headshot</th>\n",
       "      <th>total_shots_hit</th>\n",
       "      <th>total_mvps</th>\n",
       "      <th>total_wins</th>\n",
       "      <th>total_rounds_played</th>\n",
       "      <th>total_shots_fired</th>\n",
       "      <th>rank_id</th>\n",
       "      <th>goal_id</th>\n",
       "      <th>steam_id</th>\n",
       "      <th>about</th>\n",
       "      <th>updated_at</th>\n",
       "      <th>compensation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>s1rc0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>rabbitshu</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Mochojojo</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>206</td>\n",
       "      <td>BoyKot</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>7.656120e+16</td>\n",
       "      <td>None</td>\n",
       "      <td>2017-12-09 03:10:27.954734+00:00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>382</td>\n",
       "      <td>hazzard</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user_id   nickname  total_kills  total_deaths  total_time_played  \\\n",
       "0        1      s1rc0          NaN           NaN                NaN   \n",
       "1        5  rabbitshu          NaN           NaN                NaN   \n",
       "2        3  Mochojojo          NaN           NaN                NaN   \n",
       "3      206     BoyKot          NaN           NaN                NaN   \n",
       "4      382    hazzard          NaN           NaN                NaN   \n",
       "\n",
       "   total_kills_headshot  total_shots_hit  total_mvps  total_wins  \\\n",
       "0                   NaN              NaN         NaN         NaN   \n",
       "1                   NaN              NaN         NaN         NaN   \n",
       "2                   NaN              NaN         NaN         NaN   \n",
       "3                   NaN              NaN         NaN         NaN   \n",
       "4                   NaN              NaN         NaN         NaN   \n",
       "\n",
       "   total_rounds_played  total_shots_fired  rank_id  goal_id      steam_id  \\\n",
       "0                  NaN                NaN        1        1           NaN   \n",
       "1                  NaN                NaN        1        1           NaN   \n",
       "2                  NaN                NaN       10        3           NaN   \n",
       "3                  NaN                NaN       10        1  7.656120e+16   \n",
       "4                  NaN                NaN       10        3           NaN   \n",
       "\n",
       "  about                       updated_at  compensation  \n",
       "0  None                              NaT           NaN  \n",
       "1  None                              NaT           NaN  \n",
       "2  None                              NaT           NaN  \n",
       "3  None 2017-12-09 03:10:27.954734+00:00           NaN  \n",
       "4  None                              NaT           NaN  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csgo_profiles = pd.DataFrame(csgo_profiles, columns = colnames)\n",
    "# data shape\n",
    "print(\"data shape:\",csgo_profiles.shape)\n",
    "print(\"No. of users:\",csgo_profiles['user_id'].count())\n",
    "print()\n",
    "# print columns\n",
    "print(\"There are\",csgo_profiles.shape[1],\"columns:\")\n",
    "print(colnames)\n",
    "csgo_profiles.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No. of players: 75927\n",
      "No. of players: 75924\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "user_id                     0\n",
       "nickname                    0\n",
       "total_kills                 9\n",
       "total_deaths                5\n",
       "total_time_played           0\n",
       "total_kills_headshot       15\n",
       "total_shots_hit             5\n",
       "total_mvps                107\n",
       "total_wins                 11\n",
       "total_rounds_played         2\n",
       "total_shots_fired           3\n",
       "rank_id                     0\n",
       "goal_id                     0\n",
       "steam_id                    8\n",
       "about                   64770\n",
       "updated_at                  0\n",
       "compensation            75924\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Drop users who haven't played the game (total_time_played != nan)\n",
    "profiles_plyrs = csgo_profiles.dropna(axis=0, subset=['total_time_played'],how='any')\n",
    "print(\"No. of players:\",profiles_plyrs['user_id'].count())\n",
    "\n",
    "#Players must play for some time (total_time_played != 0)\n",
    "profiles_plyrs = profiles_plyrs[profiles_plyrs['total_time_played']!=0]\n",
    "print(\"No. of players:\",profiles_plyrs['user_id'].count())\n",
    "\n",
    "profiles_plyrs.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After replacement:\n",
      "\n",
      "user_id                     0\n",
      "nickname                    0\n",
      "total_kills                 0\n",
      "total_deaths                0\n",
      "total_time_played           0\n",
      "total_kills_headshot        0\n",
      "total_shots_hit             0\n",
      "total_mvps                  0\n",
      "total_wins                  0\n",
      "total_rounds_played         0\n",
      "total_shots_fired           0\n",
      "rank_id                     0\n",
      "goal_id                     0\n",
      "steam_id                    8\n",
      "about                   64770\n",
      "updated_at                  0\n",
      "compensation            75924\n",
      "dtype: int64\n",
      "\n",
      "The original:\n",
      "\n",
      "user_id                     0\n",
      "nickname                    0\n",
      "total_kills                 9\n",
      "total_deaths                5\n",
      "total_time_played           0\n",
      "total_kills_headshot       15\n",
      "total_shots_hit             5\n",
      "total_mvps                107\n",
      "total_wins                 11\n",
      "total_rounds_played         2\n",
      "total_shots_fired           3\n",
      "rank_id                     0\n",
      "goal_id                     0\n",
      "steam_id                    8\n",
      "about                   64770\n",
      "updated_at                  0\n",
      "compensation            75924\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Other Properties - Replace NA values with 0\n",
    "profiles = profiles_plyrs.copy()\n",
    "columns = ['total_kills','total_deaths','total_kills_headshot','total_shots_hit','total_mvps','total_wins','total_rounds_played','total_shots_fired']\n",
    "for c in columns:\n",
    "    profiles[c] = profiles[c].fillna(0)\n",
    "print(\"After replacement:\")\n",
    "print()\n",
    "print(profiles.isnull().sum())\n",
    "print()\n",
    "print(\"The original:\")\n",
    "print()\n",
    "print(profiles_plyrs.isnull().sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K/D ratio confidence level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a=profiles.copy() \n",
    "a.loc[a['total_deaths'] ==0,'total_deaths']=1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5     0.111111\n",
       "8     0.793251\n",
       "10    0.901163\n",
       "11    0.745455\n",
       "12    1.034535\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kill_death = profiles[\"total_kills\"]/a[\"total_deaths\"] \n",
    "kill_death.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kill_death_without_outliers=kill_death[kill_death<10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q_25 is:  0.914274615459441 , q_50 is:  1.0383350676378773 , q_75 is:  1.181094977526778\n",
      "IQR is:  0.26682036206733706\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_25 = kill_death_without_outliers.quantile(0.25)\n",
    "q_50 = kill_death_without_outliers.quantile(0.5)\n",
    "q_75 = kill_death_without_outliers.quantile(0.75)\n",
    "print(\"q_25 is: \", q_25,\", q_50 is: \", q_50,\", q_75 is: \", q_75)\n",
    "IQR = q_75-q_25\n",
    "print(\"IQR is: \",IQR)\n",
    "kill_death_without_outliers.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a14574d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a255c64e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[1.0993 - 1.1061]\n",
      "confidence interval for the variance:[0.2139 - 0.2461]\n",
      "confidence interval for the skew:[7.4288 - 8.0468]\n",
      "confidence interval for the kurtosis:[90.6183 - 103.5524]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Values less than or equal to 0 in data. Throwing out 0 or negative values\n",
      "Calculating best minimal value for power law fit\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tail split at 2.01502642007926, alpha_value = 3.483457631985346\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a13e93828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ezNQPk6lv9PJlWm+MhbrkNMA2DysNX83guvMGs7KkigN1jaR53FrBVLpMASASDrt3w8sv\nM7fYh2v/flYPO48kXxNHPKkAGGNOslXmibXcNyHFbfBZy0Vnaq6BdJ4CQCTcdu6EF19kavkA6n1+\nRu7dyYDa/Xw06Cw+zcrhoDs5bLfKyvAw5NT04Igiv0WBIO2mABDpTiUlUFQEL7wAn3zC3Ose4J0z\nRpPmayLf4+UDVybH7Y7ZQW7jrFja6LOke1xY0MQzaRcFgEgkWAubNzthUFQEn31G4fhreezCb+Jz\nJ5HmcbGP8NcMsjKSNc9A2qQAEIk0vx/+8Q8nCF56CfbsYeqtj1OflMyR1HROTzOcM3wIi7Z9GZbb\npSS5OHtgbz7bX4e1qPNYghQAItHk9cLq1U4T0Z/+BF86H/pzr3uA4pyRHExOx4vrJBc5MZcBf/OP\nb4rbcM15Q4LPnZGVoZpBAou5ADDGDAN+AmRaa69rz/coAKRHaGyEN990wuDVV6G2lsLx1/LwRXPA\nZWh0ewCDx2Vo8nf+5zHZbXC7DE0+P2nJboZl91ITUYIKawAYY54GZgF7rbWjQo5fBvwGcANPWmsf\nbMe1XlYASMKqq4OlS51momXLmHv5PZRnDuCMmi8YcEo6q/uPpNLnDsutAktRWNAeyAkm3AHwVeAw\n8L+BADDGuIFPgK8DFcAGYDZOGPyqxSW+Y63d2/x9CgARgJoa+POfnTB46y3w+Zh73QOsyxmFcbup\na64ZhDb1tFdobSLFbchISeL9+6eztqya4ooa1Qp6uLA3ARljcoGlIQFwIfAza+2lzY/vBbDWtvzw\nb3mdEwaAMeZ24HaA008//bxdu3a1q3wica2qyukrKCqCNWuYe+39Ts3gUBX7Bp2BKyuL4lqDr5Mt\nRFkZHk5JT2bXvjrunjEcgKXFuzWaqIeKRABcB1xmrb21+fHNwARr7Z1tfH8WsACnxvDkyYICVAOQ\nBFVRAX/8oxMG69cDUDj+WpaffTEfZg/F73LjcRlcLsMR78lnG7SsQQRmHwf+H1iO4h879tMrNYmz\nB/ZRJ3Kci0QAfBO4tEUAjLfW/rCzhW5JASAJr6wMXnzR6UDesoWptz5On4bDjDy8F/KGseGU0yk9\n7PwMt1xWInDsh1PzWfh2aZvnhPK4DEluw4jTeuMHhUGcitkmoHbeS5vCi7TUvN0lRUVOMIAzzyAl\nnYxeKZTSq9VvC4TAY6tK8bVjenJozcDnd0YUnXfGqZqBHEciEQBJOJ3A04DPcTqB51hrt3ayzMdR\nDUCkFdbCxo1OreDFF+Hzz5l73QOsyR2D37jA5WJaTgZkZLCipAqA/OwMSqtqO33LGyfksLumgV37\n6uiVmqQ+gxgX7lFALwBTgH7AHuABa+1TxphvAI/gjPx52lq7oEulbkEBIHISfj+88w4UFVFYcpjH\nCmYy/rMPeeqVBRRe/UPcowsotIPZ1+APjgzqzKiiYyadNc9AzkxPZlJ+Fn8v3afaQYyJuYlgHaEm\nIJFO8HphxQqniWjxYjh4EHBmH7tOOYV9p+WQNXgAAwf0YdG6cuDkfQKtCYRB79QkDjV4uXFCDguu\nLmBtWTVP/m2HRhXFgLgOgADVAEQ6qaEB/vIXp5notdegvt457nIx97bfUJ49hDNy+kNyEu9sr6ax\ng+NLs3slU3W4EXBqBEP6prGjqjbYd3DNuYMZlp1B0fpyck5NVw0hwhQAIuI4fNgJgRdecEKhqck5\n7vFQOOdulg8dR9bg/nxWcyTYTzAoM5XKmoZWL5fmcVHf5GfEgF7sqK49LjwMkBfS5zBtRDbVtY0a\nURRBCgAROd6BA07zUFERvP2204cAkJbG1Hm/pz6jD1NHD2HxB19Q39T2kKHs3slUH2pkUn4W75Tu\na/O8QDOR22VIdhuuOXcwWyoPMmPUQAqGZGpWcjeJ6wBQH4BIBOzZc3TC2d//Hjxc+NU5LD/vUg5n\nZtEnqw9bdx+i0WfJyvCwr7YpeN7YnEw2lde061bJbmcWs89vcRuYPDybDTsPMH9aPsuKd1NT7+UX\nV49SIIRJXAdAgGoAIhGya5ezh0FREbz/fvBw4SU3s/zc6cwa1Z+/+zOZdGY/zhmUyX/+pYQPKmrw\nW6fJJy3ZTX2jr80O5ZYjj5JczuPAsWkjstlUXsOMUQOCNQQFQecpAESkcz7++Ojs45KSo8cHD4br\nr4fZsyms7cvyrV/gAkqrarli9MDgyKITGTGgFyV7Dh933G1gyvBsVpRUBYeZ+kFB0EkKABHpGmuh\nuPjo7OOdO48+l5cHN9xA4VdmUDBuOE+s2UH5/jpys9JZUVKF2wVJLhdYy5EWncTDT+vNx18cAsDt\n4pjZyQbwuJ19kFOSXOT0TcNv4e27pnT7y+1J4joA1AcgEmOshXXrnFrBSy/BF18cfe6cc2D2bPjW\nt5j7t/24DAzok4rLwKJ15XjchuxeKew9dARvKzPQUpIMR7y2xTFnGQqv35nFrBDomLgOgADVAERi\nkM8Ha9Y4YfDyy87IooDzz4cbboDrr2fuW5W4DNx68TCKK2pwu+DBZSX4rPOhXlnTQF2j74S3Csxe\nvnFCDjMLBlFcUUP5/lreLduvQDgBBYCIdL/GRmczm6IiZ3Obw83t+8bAxRc7YXDddZCdTeHqMv5n\n7U6mjsgm59QMyvfXsmhdebtmI+dnZ/D5lw2MOK0Xm8prGJuTSWZ6Mrd/dZhGDrVCASAikVVXB8uW\nOWGwdCkcOeIcd7vha19zwuDqqyEzE4C5z6ynpq6RrZUHg23+jV7/cWEwoE8Kew4ewW3AZyHd46Ku\nyc+NE3JY8sFuZhUMZFh2htYkCqEAEJHoOXgQXn3VCYM333TWKQJIToZvfMPpM5g1i8INu1m+ZTcu\n4MPPa/D6W5+F7HEbmlp0Jie7DSked3AE0qkZHt7/6fQIvcDYFtcBoE5gkR6kutqZffzCC7B6tdOh\nDJCRAVdc4QwrTT+L/1lfQUaym9KqWm6ckENuvwx++XpJsEaQ5IKWG6Dl9E2j/ICzztHYnEwNHW0W\n1wEQoBqASA9TWXl0wtm6dUePn3IKXHMNU8+4hgtHDWHm6MHc+fwmxuZksqKkKvjhn5Hsorbx+CUq\nAktOpCe7efLb49haWcPS4t0JGwYKABGJbTt2OBPOioqc+QYB/ftTeOPdFEw+l3/dbslM87C5vIap\nI7L52/Z9eP3+Nvcz+MnMEQAseL0Et4H+fVJ5995pEXgxsUUBICLx46OPnCB44QUoLT16/PTTmfut\nf2fS2KHsSM5k6Ye72zXr2AX4cZaYOH9oVsItPKcAEJH4Y62zFlFg9nFFRfCpwpnfo2BsPnd5zqGy\nzn/Sxeh6pyYBMH9aPo+v2pFQ6wwpAEQkvvn9sHatEwQvvQRVzv7GU299nEzjY9OpZ5Ce5OLJW8Zz\n10sftLp/gTHgNobJZ/VjRUkV6clu/s/Xz2RHVW2P3psgrgNAo4BE5BheL6xc6TQRLV7M3K//My6/\nn1vf+zNbz7+EBflfx2CwEJwv0JLHZfjxjOEsXFGK1+fnwrwsxg/N6pEhENcBEKAagIgc58gReOMN\nJwyWLGHuN/6FT7JyqMwcwLQDZWzqNxSbnMyBBt9xYWBwagVJLmcOwe9uPq9HjhhqbwC4IlEYEZGw\nSUlx5g+88ALs3cuz144gNS2FaWXr2ZSazR1vPY3Zv59BR2rwWYvLHP1Wi7MHQaPP0r93Ck/9bQcL\nXi9h+57DFAzJ5Pd/K2PuM+uj9tIiTQEgIvErIwNuuIG3f30T5996PY8O9+MbMZIZH/+dyuTepDQ1\nMqVsAx6/j5YrDu2oqmVFSRUelwnOHVjweglf1jWytqw6eN7asmruXVxM4eqyCL+47qcmIBHpceYW\nvoPri91cuG0tCwdegNfldr7cSViM0w4UYnxuXzbsPMCc5vWFAIZlZzBqUJ/g40BzUTysOaQmIBFJ\nWM/Ou4inf/ZNfN+/k/OHD4TkZFKtn0VFP2Ha9n84w02bvwywfucBzs/ty4KrC/jdzecB8EF5DYvW\nlXOkyRf88F/wegnl++ui++LCSAEgIj3WvMl5jD97MFeNz+V335/M1l//nhVnXUCK38vU0vXkV3+G\ntRbj97Ph0/38/rmVTByWxS0Tc4PXaPRZHnnrExa87myPmZuV3mP6CZKiXYDWhAwDjXZRRCTOhY7s\neWLNDqaO6M+tFw1j68ZsVm46wLSKYqpNCll1NfyS89l53T0sOXMiqW4PDc1DiNbvdDa9mTbC2bd4\n6ojsqLyWcFMfgIgkpLnPrGdSfha3XTQM1q+HoiJ+8qmbojMvJr2pgd+9soD7Z/4TpX0G4AwgdaQk\nuZiUH9tzCNrbBxCTNQARke52TEfuhAkwYQI5K7dz/dYdXF6ynq1DR1Hau3/z4CHb3HFs8fv9vLO9\nmn21jTEbAO2lABARaTbvkjPhkjOBS/npQyuhuo7eviMcciU7J1ho8vkBQ1bVbti7F/r3j2aRu0Sd\nwCIircjJymDaiGwOuVOODhs1BjC4/H727fgMBg6E6dPhmWfgyy+jWt7OUACIiLTi2VvGU13biGn5\nhDH43S6yeqWCywVvvQXf+Q4MGABXXuksXldbG40id5gCQESkDWcP7IPHfVwEAIYLZ1/G2vUfc+8v\nXqRwzo+hqQmWLHH2O+7f3/n/q686axfFKAWAiEgbzsjK4JxBfVp9blnxbr736nb+3NCbXdfeCJ9/\nDr/5DVx4IdTVOTWBq65yagbf+Q68+aazqmkMUQCIiLRh3uQ8/DhLSbe0ubwGry9kf+KBA2H+fGcP\ng08/hQcfhNGjoabG6SO49FIYNAh+8AN45x1nv4MoUwCIiJxAVkYyTX5LerKbcwb1Dh63gDdkc+K1\nZdVHF4zLzYW774bNm53tLh94AM46y9nU5re/hYsvhjPOgLvugo0bnWUpokABICJyAvtqG0lPdvPk\nt8dx1djBxzzX5LMYYxiWncH3/rCRXfta6fwdORJ+9jMoKXG2u/yXf4GcHGe7y//6Lxg3DoYPh/vv\nd8IigmJyJrB2BBORWFG4uoyCIZkAfO8PGznS5KMxZJcZl3FmBwNcNXYwv7qm4OQX9fvhH/9w9jR4\n6SVnPkFAQQHccIPTiZyb26kya0cwEZEwKlxdxvpP9/Fu2T6afH68IU34LgMZKUnBlUSLK2raP0vY\n64VVq5xO4z/96eh8ggUL4L77OlVWLQctIhJG8ybnMaBPKgBpyUlclJ8VfM5vYf40Z/HKNpuC2pKU\nBF/7Gjz5JOzZ4wwlnTPHqQV0My0FISLSAUluF/On5bNwRSnO6kCO//zLx7hbGS3UIcnJcPnlzlcE\nqAYgItJOZ2Rl8Lubz2NHVS1en59Ujyu453Cjz3LE6yfJ7WJYdkZcbCGpABARaad5k/OYmNcPcGoC\nT809n9njc4LP+y1cMXogj6/agdtFzIeAAkBEpIMCNQGAJR/sJrTl5/l15cwYNSAuQkABICLSQYGa\nwGsfVOL1+clISSKnr9NBbIGXN37OHVOGxXwIKABERLog0Clc2+gnI9ntHHPB46t2cMeUYSxcUdqx\nUUERpAAQEemkM7IymD8tP/hh72puCwqEwcIVpQAx2ymsABAR6aR5k/Pw+Qk298yflk+ax/lYLT9Q\nT32jLxgQsdgUpAAQEemCliHwo+ln4W7+ZPX6Lb9+a3vwucCSErFCASAi0kWhIbBwRSlulyvYKVzX\n6GPhilLumDKM4oqaKJf0WAoAEZEwmDc5jx1VTmfv2QN7U36ggZy+aQCkN/cHxFpnsAJARCRMAp3C\nZVW1uF2G8gP15PRNY8/BIzR6/THXGRyxADDGXGWM+b0x5lVjzPRI3VdEJFICTUHzp+WT3LyXcPmB\nepJcBp/fsnBFaUz1A7QrAIwxTxtj9hpjtrQ4fpkx5mNjTKkx5p4TXcNa+2dr7W3AXOBbnS6xiEgM\nC4TAhXlZwc5giyU5ycX5uX1jqh+gvTWAZ4HLQg8YY9zAY8AM4GxgtjHmbGPMV4wxS1t89Q/51n9t\n/j4RkR6pYEgm75btw++HEQN64fNDo9fHhp0H4q8GYK1dA+xvcXg8UGqt3WGtbQSKgCuttR9aa2e1\n+NprHP8BLLfWvh/elyEiEjte+6CSJLeL0TmZlOw5zPDTeuP1Q352BhA78wG60gcwGCgPeVzRfKwt\nPwS+BlxnjJnX1knGmNuNMe8ZY96rqqrqQvFERKIj0Bn80e5DJLkMH39xiIvys9haeYjvPrshZkYD\ndSUAWtv5oM39Ja21C62151n+JCIvAAAMaElEQVRr51lrC09w3hPW2nHW2nHZ2dldKJ6ISHQE+gG+\ned5gfH6Lx214b9cBjHGWjL589KBoFxHoWgBUADkhj4cAlV0rjsMYc7kx5omamtjpLBER6YiCIZks\n37KH+2aOwFpoaPJzxOvnrkvPYmJeP9aWVUe9KagrAbABONMYM9QYkwzcACwJR6Gsta9Za2/PzIyd\nzhIRkY4orqjh0TljOWdQJqa5vSTJBTuqallbVs2dz2+Keodwe4eBvgC8Cww3xlQYY75rrfUCdwJv\nANuAl6y1W7uvqCIi8WPe5DzA2SQ+1ePmnEFOR/CfNlbwvT9s5NE5Y4Hodgi3a1N4a+3sNo4vA5aF\ntUQ4TUDA5fn5+eG+tIhIxLz2gdMqHtg9bO4zG2j0+jlzQDoAdz6/KRgE0RCTS0GoCUhEeoLA1pGB\n3cPcBpKTXHz8xSG+94eNUV8gLiYDQESkJwhsHbm2rJqlxbtJcruY+ZXT8PotDU2+qC8NoQAQEelm\nxRU1/O7m85g/LZ8/b6pkfG5fvD7L+bl9mZjXL2rliskA0DBQEelJAh3CD7+5nUn5/Vi/8wBXjR3M\n5vIafv+3sqh1BMdkAKgPQER6muKKGq45dxB/L63m6rGDWP1JFTNGDeDhN7dHrRkoJgNARKSnKRiS\nyeL3K5kzIYfVn1Qz+axsnl9XzjXnDopaR7ACQEQkAooravjR9DNZvmUPk8/qxyubPmdSfj8Wv18Z\ntRpAu+YBRJrmAYhITxPoBwD45esljM/ty99Lq7lv5oiodQTHZA1AfQAi0hPdu7iYhStKuWrs4GBH\n8MIVpdy7uDgq5YnJABAR6al8fstft+1h/tR8/rptDz5/m4sodzsFgIhIhFw+ehBu17Er6btdJmrL\nQ8dkH4CISE9UXFHDrIKBzizgt0uZPzWfC/KyeO2DSoorao7pJ4iEmKwBaCKYiPRE8ybnMSw7gz9v\nquTqsYN4bt1nbK2s4Y2te6IyEigmA0CdwCLSE60tq+bxVTu4b+aI4FyAX75ewh1ThkVlJJCagERE\nIiSwSczEvH4cqvey8O1Srh47GJ8/OuWJyRqAiEhPNG9yHsUVzvo/z637jPlT81n9SRVuV3Q2hlEA\niIhEkNtFsNnnR9OHc8eUYfzy9RLcUfg0VhOQiEgE+fxw38wRPL5qB4fqvTy37jPumzkiKs1AMRkA\nWgpCRHqqwFDPQB/A/Kn53HZxZId/BsRkAFhrXwNeGzdu3G3RLouISDgVri7D7SLYB/Dcus/onZaE\nz4/mAYiI9GTqAxARSVDqAxARSVDqAxARSWD3Li5mafHuYB/ABXlZABFfD0gBICISQWvLqllavBuA\nC/KyuCAvi+/9YSMAv7v5vIiWJSYDQMNARaSnKq6oCX7Q3/n8Jm6acDoAswoGRnw9IGNt9DYjOJlx\n48bZ9957L9rFEBHpFg+/+XGwH+BH04eH7brGmI3W2nEnO0/DQEVEomBtWfUxcwHWllVHvAwKABGR\nCFtbVs2dz2/i0Tlj+dH04Tw6Zyx3Pr8p4iEQk30AIiI9WWBZ6OIKZ9OriXn9jnkcqdFAqgGIiETY\nvMl5TMzrR8GQzOBv/qGPI7U7mGoAIiJREvjNPzAa6Ll1nwU3jIkE1QBERKJoYl4/bppwOgvfLuWm\nCadHdCioAkBEJIqiORpIASAiEiXRHg2kABARiZLQTeLh+NFA3S0mZwKHLAVx2/bt26NdHBGRuBLX\nM4Gtta9Za2/PzIzMUCgRkWgqXF12XLPP2rJqCleXdet9YzIAREQSSeh8ADjaN9Dd8wE0D0BEJMqi\nNR9ANQARkRgQjfkACgARkRgQjfkACgARkSiL1nwABYCISJRFaz5ATM4DCNCOYCIiHRfX8wBERKT7\nKQBERBKUAkBEJEEpAEREYkA0loNQAIiIxIBoLAehpSBERGJANJaDiFgNwBgz0hhTaIx52RhzR6Tu\nKyISLyK9HES7AsAY87QxZq8xZkuL45cZYz42xpQaY+450TWstdustfOA64GTjk8VEUk0kV4Oor01\ngGeBy0IPGGPcwGPADOBsYLYx5mxjzFeMMUtbfPVv/p4rgHeAFWF7BSIiPUA0loNoVwBYa9cA+1sc\nHg+UWmt3WGsbgSLgSmvth9baWS2+9jZfZ4m1diJwYzhfhIhIvIvGchBd6QQeDJSHPK4AJrR1sjFm\nCnANkAIsO8F5twO3A5x++uldKJ6ISPyYNznvuGMT8/p1az9AVwLAtHKszYWFrLWrgFUnu6i19gng\nCXDWAupk2URE5CS6MgqoAsgJeTwEqOxacRzGmMuNMU/U1HTvSngiIomsKwGwATjTGDPUGJMM3AAs\nCUehtCm8iEj3a+8w0BeAd4HhxpgKY8x3rbVe4E7gDWAb8JK1dmv3FVVERMKpXX0A1trZbRxfxgk6\ndDvLGHM5cHl+fn64Ly0iIs1ici0gNQGJiHS/mAwAERHpfgoAEZEEFZMBoGGgIiLdLyYDQH0AIiLd\nLyYDQEQk0WhHMBGRBKUdwZppHoCIJJoevSNYR6gPQEQSUUzuCCYiIt0vVncEExGRbhSzO4KJiEj3\nisaOYMba2NtzJaQT+Lbt27dHuzgiInHFGLPRWjvuZOfFZA1AncAiIt0vJgNARES6nwJARCRBKQBE\nRBKUAkBEJEHF9FIQwEFjTGeGAWUCWku6Y3ryexYvry2WyhmNskTqnt11n3Bftx/Q2UkAZ7TnpJgc\nBtpVxpgnrLW3R7sc8aQnv2fx8tpiqZzRKEuk7tld9wn3dY0x77VnKGdX9NQmoNeiXYA41JPfs3h5\nbbFUzmiUJVL37K77xNLfX7v0yBqAiEi8Uw1ARCRxPdHdN1ANQEQkQakGICKSoGJyGGg0GGMygN8C\njcAqa+2iKBcp5vXk96wnv7buovcs/sRUDcAYk2OMWWmM2WaM2WqM+acuXOtpY8xeY8yWVp67zBjz\nsTGm1BhzT/Pha4CXrbW3AVd09r6RZoxJNcasN8Z80Pye/bwL14rJ98wY4zbGbDLGLO3CNWLytXUH\nY8wpxpiXjTElzT9LF3byOgnzniWqmAoAwAv8X2vtSOAC4AfGmLNDTzDG9DfG9G5xrLXNg58FLmt5\n0BjjBh4DZgBnA7Ob7zEEKG8+zdfF1xFJR4Cp1trRwBjgMmPMBaEn9ID37J+Aba090QNeW3f4DfAX\na+0IYDQt3ju9Z/HJGDPMGPOUMeblcF0zpgLAWrvbWvt+858P4fzDHdzitMnAq8aYVABjzG3Awlau\ntQbY38ptxgOl1tod1tpGoAi4EqjA+QcMMfa+nIh1HG5+6Gn+atmzH7fvmTFmCDATeLKNU+L2tXUH\nY0wf4KvAUwDW2kZr7ZctTtN7FiPaqmW1VsNqfr+/G877x+xfkjEmFxgLrAs9bq39I/AXoMgYcyPw\nHeD6Dlx6MEd/SwHnH+1gYDFwrTHmceJsQkdzE8lmYC/wlrW2J71njwA/BvytPRnnr607DAOqgGea\nm82ebG6bD9J7FlOepUUt6wQ1rLCLyU5gY0wv4E/AP1trD7Z83lr7/4wxRcDjQF7Ib8Dtunwrx6y1\ntha4pVMFjjJrrQ8YY4w5BXjFGDPKWrulxTlx954ZY2YBe621G40xU9o6Lx5fWzdKAs4FfmitXWeM\n+Q1wD/DT0JP0nsUGa+2a5l92QwVrWADNf09XAh+F+/4xVwMwxnhwPvwXWWsXt3HOxcAo4BXggQ7e\nogLICXk8BKjsRFFjTnNVfxWtt9vG43s2CbjCGLMTp5lhqjHmuZYnxelr6y4VQEVILfBlnEA4ht6z\nmNZqDcsYk2WMKQTGGmPuDceNYioAjDEGp+1ym7X24TbOGQv8HicRbwFONcb8ogO32QCcaYwZaoxJ\nBm4AlnSt5NFjjMlu/s0fY0wa8DWgpMU5cfmeWWvvtdYOsdbmNt/zbWvtTaHnxOtr6y7W2i+AcmPM\n8OZD02jxm6Pes5jXVg1rn7V2nrU2z1r7q3DcKKYCAOc3vptxftPb3Pz1jRbnpAPftNaWWWv9wLeB\nXS0vZIx5AXgXGG6MqTDGfBfAWusF7gTewOlkfslau7X7XlK3GwisNMYU4/xgvmWtbTlcsie/Zz35\ntXXWD4FFzf8mxgC/bPG83rPYFrEalpaCEBGJouY+gKXW2lHNj5OAT3Bqb5/j/GI3pztCNtZqACIi\nCaO1WlYka1iqAYiIJCjVAEREEpQCQEQkQSkAREQSlAJARCRBKQBERBKUAkBEJEEpAEREEpQCQEQk\nQSkAREQS1P8HaUvfZnH7KZMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a248c7b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<scipy.stats._continuous_distns.expon_gen object at 0x110d3e400>\n",
      "<scipy.stats._continuous_distns.norm_gen object at 0x110d14e48>\n",
      "<scipy.stats._continuous_distns.logistic_gen object at 0x110d144a8>\n",
      "<scipy.stats._continuous_distns.t_gen object at 0x110e030f0>\n",
      "<scipy.stats._continuous_distns.chi2_gen object at 0x110d359e8>\n",
      "<scipy.stats._continuous_distns.dweibull_gen object at 0x110d3e1d0>\n",
      "<scipy.stats._continuous_distns.beta_gen object at 0x110d25400>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/weisihan/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py:161: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<scipy.stats._continuous_distns.lognorm_gen object at 0x110df0908>\n",
      "<scipy.stats._continuous_distns.gamma_gen object at 0x110dc2fd0>\n",
      "<scipy.stats._continuous_distns.skew_norm_gen object at 0x110e277f0>\n",
      "<scipy.stats._continuous_distns.f_gen object at 0x110dad2b0>\n",
      "<scipy.stats._continuous_distns.powerlaw_gen object at 0x110e03d68>\n",
      "<scipy.stats._continuous_distns.pareto_gen object at 0x110e035f8>\n"
     ]
    }
   ],
   "source": [
    "res=pipeline_(kill_death_without_outliers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# it has a long tail because the data contains a lot of outliers\n",
    "# so we have to remove them\n",
    "# this is the function to remove the outliers and calculate the suitbale bin width\n",
    "def del_outlier (col_of_df):\n",
    "    q_25 = col_of_df.quantile(0.25)\n",
    "    q_50 = col_of_df.quantile(0.5)\n",
    "    q_75 = col_of_df.quantile(0.75)\n",
    "    print(\"q_25 is: \", q_25,\", q_50 is: \", q_50,\", q_75 is: \", q_75)\n",
    "    IQR = q_75-q_25\n",
    "    print(\"IQR is: \",IQR)\n",
    "   \n",
    "    # removing outliers from the data: We only accept data smaller than Q3+3*IQR and larger than Q1-3*IQR\n",
    "    profiles_without_outlier = col_of_df[np.logical_and(col_of_df <= q_75 + 3*IQR, col_of_df >= q_25 - 3*IQR)]\n",
    "    \n",
    "    # optimal width of bins is equal to: 2*IQR*n^(-1/3), n is the number of observations\n",
    "    width = 2*IQR*np.power(len(profiles_without_outlier),-1/3)\n",
    "    print(\"bin width is: \", width)\n",
    "    \n",
    "    return profiles_without_outlier, width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Total time played confidence level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75924"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_time=profiles[\"total_time_played\"]\n",
    "total_time.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q_25 is:  652465.75 , q_50 is:  1489140.0 , q_75 is:  2785035.5\n",
      "IQR is:  2132569.75\n",
      "bin width is:  100979.016524\n"
     ]
    }
   ],
   "source": [
    "total_time_played_without_outlier, bins=del_outlier (total_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q_25 is:  10874.429166666667 , q_50 is:  24819.0 , q_75 is:  46417.25833333333\n",
      "IQR is:  35542.82916666666\n",
      "bin width is:  1682.98360873\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "153018.71666666667"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_time_played_without_outlier1, bins1=del_outlier (total_time/60)\n",
    "total_time_played_without_outlier1.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X48OMDIJTtYG4QdtHx4CezuUoyaUG0A7UpD2eDOzPrTg9NBuoiIzE8rl1/Osrv8rotA6B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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a22ccea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Jv16YLc5ps37z1kOzxdrqPagfWsYZEQ9FxBnpw4/Xqcife3sd4ChKp9Qc5OLi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\nABn6/8cMZ4hRu0a8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25235c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[31866.0012 - 32265.7652]\n",
      "confidence interval for the variance:[766091498.8537 - 787827942.2346]\n",
      "confidence interval for the skew:[1.3092 - 1.3464]\n",
      "confidence interval for the kurtosis:[1.6508 - 1.8099]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating best minimal value for power law fit\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-42-717487564812>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mres\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpipeline_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtotal_time_played_without_outlier1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-39-1969ee7136eb>\u001b[0m in \u001b[0;36mpipeline_\u001b[0;34m(data, distribution, Bootstrap, tail_analysis)\u001b[0m\n\u001b[1;32m     37\u001b[0m         \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloglog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\"x\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m         \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mseterr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdivide\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ignore'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minvalid\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ignore'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m         \u001b[0mfit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpowerlaw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     40\u001b[0m         \u001b[0mtail_split\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Tail split at {}, alpha_value = {}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtail_split\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, discrete, xmin, xmax, verbose, fit_method, estimate_discrete, discrete_approximation, sigma_threshold, parameter_range, fit_optimizer, xmin_distance, **kwargs)\u001b[0m\n\u001b[1;32m    132\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m                 \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Calculating best minimal value for power law fit\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstderr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 134\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_xmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    135\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    136\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m>=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfind_xmin\u001b[0;34m(self, xmin_distance)\u001b[0m\n\u001b[1;32m    231\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 233\u001b[0;31m         \u001b[0mfits\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfit_function\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmins\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    234\u001b[0m         \u001b[0;31m# logging.warning(fits.shape)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    235\u001b[0m         \u001b[0msetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m's'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfits\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfit_function\u001b[0;34m(xmin)\u001b[0m\n\u001b[1;32m    228\u001b[0m                            \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    229\u001b[0m                            \u001b[0mparameter_range\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparameter_range\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 230\u001b[0;31m                            parent_Fit=self)\n\u001b[0m\u001b[1;32m    231\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, estimate_discrete, **kwargs)\u001b[0m\n\u001b[1;32m   1108\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1109\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1110\u001b[0;31m         \u001b[0mDistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1111\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1112\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mparameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, xmin, xmax, discrete, fit_method, data, parameters, parameter_range, initial_parameters, discrete_approximation, parent_Fit, **kwargs)\u001b[0m\n\u001b[1;32m    605\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    606\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mparameter_range\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparent_Fit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 607\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    608\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    609\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m   1139\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1140\u001b[0m                 \u001b[0mDistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msuppress_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1141\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mKS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1142\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiscrete\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmax\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1143\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mKS\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m    696\u001b[0m                             \u001b[0;34m(\u001b[0m\u001b[0mCDF_diff\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    697\u001b[0m                             \u001b[0;34m(\u001b[0m\u001b[0mTheoretical_CDF\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mTheoretical_CDF\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 698\u001b[0;31m                             )[1:]\n\u001b[0m\u001b[1;32m    699\u001b[0m                            )\n\u001b[1;32m    700\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "res=pipeline_(total_time_played_without_outlier1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### hit shot rate Confidence level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b=profiles.copy() \n",
    "b.loc[b['total_shots_fired'] ==0,'total_shots_fired']=1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5     0.727273\n",
       "8     0.176158\n",
       "10    0.174500\n",
       "11    0.107234\n",
       "12    0.195682\n",
       "dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hit_fired = profiles[\"total_shots_hit\"]/a[\"total_shots_fired\"] \n",
    "hit_fired.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#hit_fired_without_outliers,binwidth = del_outlier (hit_fired)\n",
    "hit_fired_without_outliers = hit_fired[hit_fired<1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q_25 is:  0.16754585027759356 , q_50 is:  0.1845556539805461 , q_75 is:  0.202654709616771\n",
      "IQR is:  0.035108859339177456\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_25 = hit_fired_without_outliers.quantile(0.25)\n",
    "q_50 = hit_fired_without_outliers.quantile(0.5)\n",
    "q_75 = hit_fired_without_outliers.quantile(0.75)\n",
    "print(\"q_25 is: \", q_25,\", q_50 is: \", q_50,\", q_75 is: \", q_75)\n",
    "IQR = q_75-q_25\n",
    "print(\"IQR is: \",IQR)\n",
    "hit_fired_without_outliers.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a230d0320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9loojuP/N9pO6qL+V/SNiS1rux5L2S+W7pUd5Wwf3oF6p+AKgfFuUgySdbvtr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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25a1d7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[0.1860 - 0.1865]\n",
      "confidence interval for the variance:[0.0010 - 0.0011]\n",
      "confidence interval for the skew:[3.4013 - 5.3371]\n",
      "confidence interval for the kurtosis:[59.7971 - 103.0568]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Values less than or equal to 0 in data. Throwing out 0 or negative values\n",
      "Calculating best minimal value for power law fit\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36min_range\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    908\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 909\u001b[0;31m             \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_range_dict\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    910\u001b[0m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Power_Law' object has no attribute '_range_dict'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36min_range\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    921\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 922\u001b[0;31m                 \u001b[0min_range\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_in_given_parameter_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    923\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Power_Law' object has no attribute '_in_given_parameter_range'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-41-86f8385fb67d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mres\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpipeline_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhit_fired_without_outliers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-39-1969ee7136eb>\u001b[0m in \u001b[0;36mpipeline_\u001b[0;34m(data, distribution, Bootstrap, tail_analysis)\u001b[0m\n\u001b[1;32m     37\u001b[0m         \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloglog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\"x\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m         \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mseterr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdivide\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ignore'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minvalid\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ignore'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m         \u001b[0mfit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpowerlaw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     40\u001b[0m         \u001b[0mtail_split\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Tail split at {}, alpha_value = {}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtail_split\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, discrete, xmin, xmax, verbose, fit_method, estimate_discrete, discrete_approximation, sigma_threshold, parameter_range, fit_optimizer, xmin_distance, **kwargs)\u001b[0m\n\u001b[1;32m    132\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m                 \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Calculating best minimal value for power law fit\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstderr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 134\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_xmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    135\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    136\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m>=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfind_xmin\u001b[0;34m(self, xmin_distance)\u001b[0m\n\u001b[1;32m    231\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 233\u001b[0;31m         \u001b[0mfits\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfit_function\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmins\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    234\u001b[0m         \u001b[0;31m# logging.warning(fits.shape)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    235\u001b[0m         \u001b[0msetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m's'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfits\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfit_function\u001b[0;34m(xmin)\u001b[0m\n\u001b[1;32m    228\u001b[0m                            \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    229\u001b[0m                            \u001b[0mparameter_range\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparameter_range\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 230\u001b[0;31m                            parent_Fit=self)\n\u001b[0m\u001b[1;32m    231\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, estimate_discrete, **kwargs)\u001b[0m\n\u001b[1;32m   1108\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1109\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1110\u001b[0;31m         \u001b[0mDistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1111\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1112\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mparameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, xmin, xmax, discrete, fit_method, data, parameters, parameter_range, initial_parameters, discrete_approximation, parent_Fit, **kwargs)\u001b[0m\n\u001b[1;32m    605\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    606\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mparameter_range\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparent_Fit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 607\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    608\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    609\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m   1139\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1140\u001b[0m                 \u001b[0mDistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msuppress_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1141\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mKS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1142\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiscrete\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmax\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1143\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mKS\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m    682\u001b[0m             \u001b[0mbins\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mActual_CDF\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcdf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    683\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 684\u001b[0;31m         \u001b[0mTheoretical_CDF\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcdf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbins\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    685\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    686\u001b[0m         \u001b[0mCDF_diff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTheoretical_CDF\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mActual_CDF\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mcdf\u001b[0;34m(self, data, survival)\u001b[0m\n\u001b[1;32m    751\u001b[0m         \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    752\u001b[0m         \u001b[0;32mfrom\u001b[0m \u001b[0msys\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mfloat_info\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 753\u001b[0;31m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    754\u001b[0m             \u001b[0;32mfrom\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtile\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    755\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mtile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mfloat_info\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmin_10_exp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36min_range\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    922\u001b[0m                 \u001b[0min_range\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_in_given_parameter_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    923\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 924\u001b[0;31m                 \u001b[0min_range\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_in_standard_parameter_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    925\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mbool\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    926\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m_in_standard_parameter_range\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1127\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1128\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_in_standard_parameter_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1129\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1130\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1131\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "res=pipeline_(hit_fired_without_outliers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### winning Rate confidence level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c=profiles.copy() \n",
    "c.loc[c['total_rounds_played'] ==0,'total_rounds_played']=1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((c[\"total_rounds_played\"]==0)==True).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5     0.125000\n",
       "8     0.507693\n",
       "10    0.549020\n",
       "11    0.550000\n",
       "12    0.506329\n",
       "dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "win_rounds = profiles[\"total_wins\"]/c[\"total_rounds_played\"] # this is kill per second\n",
    "win_rounds.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#win_rounds_without_outliers,binwidth = del_outlier (win_rounds)\n",
    "win_rounds_without_outliers = win_rounds[win_rounds<1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8swPv18XA8zv09/NS4D3Ag9rHx0y6D7Vx/CjwNODAKs8/Evgc8OhJxT1AjK8D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\nJEnqGBM1SZIkSeqY/x+EoQKOi0fOlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25b39630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[0.5084 - 0.5093]\n",
      "confidence interval for the variance:[0.0033 - 0.0035]\n",
      "confidence interval for the skew:[1.8390 - 2.2567]\n",
      "confidence interval for the kurtosis:[21.7193 - 23.1797]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Values less than or equal to 0 in data. Throwing out 0 or negative values\n",
      "Calculating best minimal value for power law fit\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-40-2e3f9b99f692>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mres\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpipeline_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwin_rounds_without_outliers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-39-1969ee7136eb>\u001b[0m in \u001b[0;36mpipeline_\u001b[0;34m(data, distribution, Bootstrap, tail_analysis)\u001b[0m\n\u001b[1;32m     37\u001b[0m         \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloglog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\"x\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m         \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mseterr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdivide\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ignore'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minvalid\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ignore'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m         \u001b[0mfit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpowerlaw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     40\u001b[0m         \u001b[0mtail_split\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Tail split at {}, alpha_value = {}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtail_split\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, discrete, xmin, xmax, verbose, fit_method, estimate_discrete, discrete_approximation, sigma_threshold, parameter_range, fit_optimizer, xmin_distance, **kwargs)\u001b[0m\n\u001b[1;32m    132\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m                 \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Calculating best minimal value for power law fit\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstderr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 134\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_xmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    135\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    136\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m>=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfind_xmin\u001b[0;34m(self, xmin_distance)\u001b[0m\n\u001b[1;32m    231\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 233\u001b[0;31m         \u001b[0mfits\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfit_function\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmins\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    234\u001b[0m         \u001b[0;31m# logging.warning(fits.shape)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    235\u001b[0m         \u001b[0msetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m's'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfits\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfit_function\u001b[0;34m(xmin)\u001b[0m\n\u001b[1;32m    228\u001b[0m                            \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    229\u001b[0m                            \u001b[0mparameter_range\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparameter_range\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 230\u001b[0;31m                            parent_Fit=self)\n\u001b[0m\u001b[1;32m    231\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, estimate_discrete, **kwargs)\u001b[0m\n\u001b[1;32m   1108\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1109\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1110\u001b[0;31m         \u001b[0mDistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1111\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1112\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mparameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, xmin, xmax, discrete, fit_method, data, parameters, parameter_range, initial_parameters, discrete_approximation, parent_Fit, **kwargs)\u001b[0m\n\u001b[1;32m    605\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    606\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mparameter_range\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparent_Fit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 607\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    608\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    609\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m   1139\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1140\u001b[0m                 \u001b[0mDistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msuppress_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1141\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mKS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1142\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiscrete\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmax\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1143\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/powerlaw.py\u001b[0m in \u001b[0;36mKS\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m    696\u001b[0m                             \u001b[0;34m(\u001b[0m\u001b[0mCDF_diff\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    697\u001b[0m                             \u001b[0;34m(\u001b[0m\u001b[0mTheoretical_CDF\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mTheoretical_CDF\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 698\u001b[0;31m                             )[1:]\n\u001b[0m\u001b[1;32m    699\u001b[0m                            )\n\u001b[1;32m    700\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "res=pipeline_(win_rounds_without_outliers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nick's code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "lWPIZchzNV6A"
   },
   "outputs": [],
   "source": [
    "head_shots_filt=cleaned_data.total_kills_headshot\n",
    "head_shots_filt=head_shots_filt[head_shots_filt!= max(head_shots_filt)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "output_extras": [
      {},
      {},
      {},
      {},
      {},
      {},
      {},
      {},
      {}
     ]
    },
    "colab_type": "code",
    "id": "0xVcYI1aNV6D",
    "outputId": "99418b67-6f0f-41a8-99b6-b2674092e366"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OOemSvJ1tb9smjlu14eU4g8TRGMsSSWfavknS4ZI+afvFI4rl4Tgi4r65yw6i\neFHlph3WyTC3zQaxqDgy9c2I+HVE3CnpQkl7jDCWsWF7UxVJzOkRcXaTUVqty7HQxfK9WsWlnRER\nN0j6qTJp3HuVLglZKenghkEP7/dpH99KxT4/Vtosn2wfJOltkl4UEb8bdWwD2FfSi9Lv95mSnmv7\nsw3j5Lj9OsYdEXeVtsVnVBzwyUJE3Jr+3iHpyyr+qS9r1VbUqlPcbdrheaX0W/Es5dG2b1RfJP17\nJrG12q9un7vcN/2t47aHWyTdUrqK4ksqErccYpvzQkmXRcTtqb+W2EaeqNnepdR7qKRrU/lOks6W\ndHRE/Lg0zg8l7eLiCTqPVnEa8pyUza5UkcBI0jGSvjqEOP5k7h4BF0+DeoyKhvObkp5ve+v0pJfn\nq/gnd52k+2zvk6Z7ZS9xtIslIp4SEVMRMaViJ/67iPhKVbG0WSd/XFone6vYb+5SRdumXSxpPvvZ\nXmD7jyQ9U8X9SZXFMo7S9jpZ0jUR8eEWo7Val9nrcvl+ruL6ctleJGlXFQ/eGQu2F9p+fOp+rKTn\n6ZF6MOccFfu0VOzj3077fPa6WT7be0r6lIokbWzuoZSkiPjniNgh/X4foWLbvKJhtOy2Xzdxe8N7\nul6kTH43bG9ue8u5bhVt49qG0c6R9EoX9pF0b+lyplp0E3ebdnjitfituEYZtO0t6stROcTWZr8q\n/+7Utd5uk3Sz7V1T0YEqHm5We2wlR+qRyx6lumKLap+WcoakdZL+oCJ7Pk7FEfC1kq5QcfnE9mnc\nz0i6R8WlSmskrSrN5xAVT3X7iaS3lcp3VvGUwxtUnJp8zBDieIukq1IMP1Bx2nhuPsem77pB0qtL\n5UvSvH6i4r4YD2OdNEy3Qumpj8OIpcd1cnxaJ5eruKH/2cPaNv2sE0n/qKJCr1VxydvQYpmUj6T9\nVJyWv6JUpw6R9DpJr+u0LnP/dLN8Ki55PE/F/WlrJb2i7rh7XManS/pRWsa1kt6Ryt+lInGRpM3S\nPn1D2sd3rjvuIS/ftyTdXtrG59Qdd5/Lur8eeRrc2Gy/NnH/a6lNWClpt7pjTXHtnGK6PMX3tlRe\n/l2wpE+kduJKSUvGJO6W7fCkf9r8VmTVtjfUl9pja7NfPUHSBZKuT7+x29S0vhZLWpW261dUPMU8\nl9g2V3EgZKtSWS2xzT2GHgAAAACQibrvUQMAAAAANCBRAwAAAIDMkKgBAAAAQGZI1AAAlbJ9iu07\nbDc+ga/ZuDvZXplegnqF7UNGESMAALkhUQMAVG2FmrwjrYW3S/pCFC9BPULSJ6sKCgCAnJGoAUAX\nbJ879y4f9CYiLpR0d7nM9lOdL3UKAAAG4UlEQVRtf8P2atvftT33MvKQ9LjUvZWkX4wwVNTI9k3z\n8SXOwCBsT3VztUKb6U9M71LtZ9p32T6o3+9GZzyeHwDaSC+ZdUQ8VHcs48z2lIp3DP156r9AxTui\nrrf9TEn/GhHPTS9TPk/FO3U2l3RQRKyuKWyMkO2bVLzX7M66YwHGReNva4/TbqLinYLUu0xxRm0M\npKMl19peYfvHtk+3fZDt79m+3vbe6Q30p9i+NN3bcWhp2u/avix9np3K97c9a/tLad6np39IgYlk\n+32231Dqf6ftt9u+INWNKxvqzXW2T1PxgtUdy0f7bX8lnQm6yvbS0jx/Zfu9ti+3fbHtRal8ke0v\np/LLS/XwFanOrrH9qdRoTjzbW0h6tqQv2l4j6VOStkuDj5S0IiJ2UPES8/9nm7ZqwqQ2aybVh7W2\n/6Y07LG2v277b1P/RvXE9kttfzgNP8H2jal7Z9vfq2epgHql/f9Htv/R9sdL5V+zvX/q/pXtD9m+\nXNLbJD1J0krbK9PwI1N7uNb2+1PZJul/0LVp2BtT+Qrbh6fu99m+2sW9xR8c7ZJPrgV1B4Cu/Ymk\nl0o6VtIPJb1c0n6SXiTprZKulvTtiDg2XZ51qe1vSbpD0vMi4re2d5F0hqQlaZ57SnqaikuLvidp\nX0kXjW6RgJH6vKSPSvpE6n+ZpBdI+lhE3JeSsIttn5OG7yLpmIi4WJIajmMcGxF3236spB/aPisi\n7lJxBujiiHib7Q9I+ltJ75H0MUnfiYjDUjK2he0/k/Q3kvaNiD/Y/qSkoySdVt0qyMajJP0yIhY3\nGXac0v1sEfED25tJ2lbFbxkmx8GSfhERfyVJtreS9H5JW0g6U9JpEXFam3pynqR/SvP6S0l32d4+\ndV842kUB6md7VxV151Uq/r97cotRN5d0SUS8OU13rKQDIuJO209SUQ+fIekeSefZfrGkmyVtX7oi\nYoPbAGw/QdJhknaLiGgcjv5xlHJ8/DQirkyXX10l6YIorlu9UtKUpOdLmk5Hp2clbSZpJ0mbSvq0\n7SslfVHS7qV5XhoRt6R5rknzASZSRPxI0hNtP8n2Hioaodsk/V/bV0j6lqTtJS1Kk/xsLklr4h/S\n0ciLJe2oIqmTpN9L+lrqXq1H6tRzJZ2U4ngwIu6VdKCKxvCHqd4eKGnnYSxr7iLiPkk/tf1Sqbi8\nNG0TSfq5inWh9E/6ZpLW1xIoqnSlpOfZfr/tv0x1QpK+Kum/ImLugEXTehIRt6k44LGlijr4OUnP\nUZGofXeUCwJkYKGKunNURFzeYdwHJZ3VYthfSJqNiPUR8YCk01XUqxsl7Wz7P2wfLOm+hunulfRb\nSSfb/l+SftPncqABZ9TGx+9K3Q+V+h9SsR0flPSSiLiuPJHtd0q6XdIeKhLz37aY54Nif8Dk+6Kk\nwyX9sYozbEepaOCekY7W36QiMZCkXzebQbp85CBJz4qI39ieLU3zh3jkxt9OdcqSTo2If+57acaE\n7TMk7S9pW9u3SPoXFev+JNtvV3FA6UxJl0t6s4qDS29U8WCRV5XWKSZERPzY9l4qLm99j4t7FqXi\n6o6DbX8ubfd29eT7kl4t6ToVydmxkp6lYh8C5pN7VRzk2k/FFVYPaMOTMZuVun8bEQ/2MvOIuCcd\nTHuBpNepuCLl2NLwB2zvreJAyuGSjldxgBID4oza5PimpL93uj7L9p6pfCtJ69JZs6MlzYt7YIAW\nPq/ike+Hq0jatpJ0R0rSDlDrS0XKtpJ0T0rSdpO0TxfTXCDp9dLD1/pvlcoOt/3EVL6N7W6+f+xE\nxJERsV1EbBoRO0TEyRHx04g4OCL2iIjdI+JdadyrI2LfVL44Is6rO34MX7rE6jcR8VlJ/yZprzTo\nHSrOds9dotyunnxX0v9WcanjjyQdIOl3pbNzwHzxexWXHr7S9ssl3SRpse1H2d5R0t5tpr1f0pap\n+1JJ/9P2tuky/SMlfSfdGvCoiDhLxStU9irPIN13vFVEnCvpjSpODmAISNQmx7tVHJW+wvZVqV8q\n3kF0TLpMaze1OEsAzAcRcZWKBunWiFin4rKOJenS4FdKuraL2XxD0gLb10h6n4rLHzs5QdIB6XtW\nS9o9Iq5W0eCdly69PF+PPFADmHT/Q8W91GtUnGF9T2nYCZIea/sDHerJd1Vc9nhhOkNws7jPGvNU\nRPxa0l+rSJSeIOmnKs6ufUzSZW0mXS7pG7ZXpnZxWtJKFVc4rI6Ir6q4LWA21dfPSmo8w72lpK+l\nOnqRpDcNbcHmOR7PDwAAAACZ4YwaAAAAAGSGRA0AAAAAMkOiBgAAAACZIVEDAAAAgMyQqAEAAABA\nZkjUAAAAACAzJGoAAAAAkJn/D9h4LFAfVEhkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111438ba8>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[13296.95 - 13542.87]\n",
      "confidence interval for the variance:[272270341.54 - 301896289.03]\n",
      "confidence interval for the skew:[  4.24 -   5.28]\n",
      "confidence interval for the kurtosis:[ 37.26 -  62.15]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating best minimal value for power law fit\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tail split at 76878.0, alpha_value = 4.20060513321088\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e2c0518>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HeatzGDprZSiaLyLVFJYBwRgz2hjzeFFRUaibIuV8evdwbh3Sg9PbR3FBQgy9O7f3PRHo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\nGd46AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3b3470>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<scipy.stats._continuous_distns.expon_gen object at 0x10a365b70>\n",
      "<scipy.stats._continuous_distns.norm_gen object at 0x109242550>\n",
      "<scipy.stats._continuous_distns.logistic_gen object at 0x10a436b00>\n",
      "<scipy.stats._continuous_distns.t_gen object at 0x10a4518d0>\n",
      "<scipy.stats._continuous_distns.chi2_gen object at 0x10a3651d0>\n",
      "<scipy.stats._continuous_distns.dweibull_gen object at 0x10a365908>\n",
      "<scipy.stats._continuous_distns.beta_gen object at 0x10a34ccc0>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/scipy/optimize/minpack.py:161: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<scipy.stats._continuous_distns.lognorm_gen object at 0x10a441198>\n",
      "<scipy.stats._continuous_distns.gamma_gen object at 0x10a4157f0>\n",
      "<scipy.stats._continuous_distns.skew_norm_gen object at 0x10a46ac88>\n",
      "<scipy.stats._continuous_distns.f_gen object at 0x10a3e7a58>\n",
      "<scipy.stats._continuous_distns.powerlaw_gen object at 0x10a45e5c0>\n",
      "<scipy.stats._continuous_distns.pareto_gen object at 0x10a451e10>\n"
     ]
    }
   ],
   "source": [
    "res=pipeline_(head_shots_filt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "output_extras": [
      {}
     ]
    },
    "colab_type": "code",
    "id": "yA55B9vaNV6O",
    "outputId": "4b265a74-7b30-4b32-ec2e-bb5a672886cd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(        dist                                              parms       loglik\n",
       " 0      expon                               (1.0, 13420.9877912)       754628\n",
       " 1       norm                     (13421.9874579, 16929.3181367)       801406\n",
       " 2   logistic                     (10689.7508481, 7078.70440253)       784906\n",
       " 3          t      (1.86561949545, 8100.53182625, 6625.75189318)       775834\n",
       " 4       chi2              (0.00130103553024, 1.0, 4.5225621692)  1.07754e+08\n",
       " 5   dweibull            (0.861397984736, 7090.0, 8950.79397007)       780012\n",
       " 6       beta  (0.891640528092, 651.613500423, 1.0, 9819693.0...       754306\n",
       " 7    lognorm                 (7.2991179942, 1.0, 10.4390426166)       874040\n",
       " 8      gamma     (320.445578159, -483403.163576, 1547.47760038)       813235\n",
       " 9   skewnorm      (707432924.669, 0.999863873502, 21603.561653)       769128\n",
       " 10         f  (702179.927348, 4.02157741999, -3039.8932781, ...       756839\n",
       " 11  powerlaw               (0.252987137826, 1.0, 403750.193364)       808018\n",
       " 12    pareto    (0.126018211249, -1.56445227046, 2.56445217729)       856191,\n",
       " <powerlaw.Fit at 0x10d7645c0>)"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "lEr_FmcuNV6T"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "output_extras": [
      {},
      {}
     ]
    },
    "colab_type": "code",
    "id": "MqYyMoSPNV6V",
    "outputId": "a3e2cdf1-de09-4140-a6b4-0d723e4d6886"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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R8D7ghNGEJamLfU0aP/uZNJxB+tAJwJnN8AeBY5JkgjFKM2WYRO1g4Btd4zc2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\nkiRJLWOiJkmSJEkt8/8Da1A0aYTt3zAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106b0a90>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[3514.15 - 3565.85]\n",
      "confidence interval for the variance:[12111600.82 - 12975223.40]\n",
      "confidence interval for the skew:[  2.33 -   3.18]\n",
      "confidence interval for the kurtosis:[ 10.64 -  30.96]\n"
     ]
    }
   ],
   "source": [
    "data=total_mvps\n",
    "iteration = 5000\n",
    "\n",
    "len_=len(data)\n",
    "mean=[]\n",
    "var=[]\n",
    "skew=[]\n",
    "kurto=[]\n",
    "\n",
    "for i in range( iteration ):\n",
    "    samp=np.random.choice(data,len_,replace=True)\n",
    "    mean.append(np.mean(samp))\n",
    "    var.append(np.var(samp))\n",
    "    skew.append(stats.skew(samp))\n",
    "    kurto.append(stats.kurtosis(samp))\n",
    "figure,[a,b,c,d]=plt.subplots(1, 4,figsize=(15,5))\n",
    "a.hist(mean,1000,label='mean')\n",
    "a.set_xlabel(\"mean\")\n",
    "b.hist(var,1000,label='variance',color='r')\n",
    "b.set_xlabel(\"variance\")\n",
    "c.hist(skew,1000,label='skew',color='y')\n",
    "c.set_xlabel(\"skew\")\n",
    "d.hist(kurto,1000,label='kurtosis',color='g')\n",
    "d.set_xlabel(\"kurtosis\")\n",
    "plt.show()\n",
    "print(\"confidence interval for the mean:[%6.2f - %6.2f]\" % (np.percentile(mean,2.5),np.percentile(mean,97.5)))\n",
    "print(\"confidence interval for the variance:[%6.2f - %6.2f]\" % (np.percentile(var,2.5),np.percentile(var,97.5)))\n",
    "print(\"confidence interval for the skew:[%6.2f - %6.2f]\" % (np.percentile(skew,2.5),np.percentile(skew,97.5)))\n",
    "print(\"confidence interval for the kurtosis:[%6.2f - %6.2f]\" % (np.percentile(kurto,2.5),np.percentile(kurto,97.5)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "output_extras": [
      {}
     ]
    },
    "colab_type": "code",
    "id": "52c6x3t6NV6c",
    "outputId": "08996af7-d6d8-4bc9-c5df-fbc446ae1b4f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e600358>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(total_mvps)\n",
    "plt.show()  # still some fake datas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "output_extras": [
      {},
      {},
      {},
      {},
      {},
      {},
      {},
      {},
      {},
      {}
     ]
    },
    "colab_type": "code",
    "id": "B9UkkoqzNV6g",
    "outputId": "087bca57-90b3-4c4c-e4c4-d204c8cb5886"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a34fd0>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for the mean:[3513.79 - 3565.50]\n",
      "confidence interval for the variance:[12123083.49 - 12963858.48]\n",
      "confidence interval for the skew:[  2.34 -   3.19]\n",
      "confidence interval for the kurtosis:[ 10.95 -  31.23]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating best minimal value for power law fit\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tail split at 18073.0, alpha_value = 5.734898987508731\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113a60eb8>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zffHW8tlIJwUVpQLAlgFAS0Eou/D9he6bMur78K42CACkpcGKFfD44xATA/Pm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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e647978>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<scipy.stats._continuous_distns.expon_gen object at 0x10a365b70>\n",
      "<scipy.stats._continuous_distns.norm_gen object at 0x109242550>\n",
      "<scipy.stats._continuous_distns.logistic_gen object at 0x10a436b00>\n",
      "<scipy.stats._continuous_distns.t_gen object at 0x10a4518d0>\n",
      "<scipy.stats._continuous_distns.chi2_gen object at 0x10a3651d0>\n",
      "<scipy.stats._continuous_distns.dweibull_gen object at 0x10a365908>\n",
      "<scipy.stats._continuous_distns.beta_gen object at 0x10a34ccc0>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/scipy/optimize/minpack.py:161: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<scipy.stats._continuous_distns.lognorm_gen object at 0x10a441198>\n",
      "<scipy.stats._continuous_distns.gamma_gen object at 0x10a4157f0>\n",
      "<scipy.stats._continuous_distns.skew_norm_gen object at 0x10a46ac88>\n",
      "<scipy.stats._continuous_distns.f_gen object at 0x10a3e7a58>\n",
      "<scipy.stats._continuous_distns.powerlaw_gen object at 0x10a45e5c0>\n",
      "<scipy.stats._continuous_distns.pareto_gen object at 0x10a451e10>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(        dist                                              parms  loglik\n",
       " 0      expon                    (0.999999999968, 3538.68150083)  658230\n",
       " 1       norm                     (3539.68160348, 3539.38138825)  688311\n",
       " 2   logistic                     (3019.86615218, 1727.47306361)  680639\n",
       " 3          t       (2.76340522226, 2635.1339802, 2074.83202128)  677702\n",
       " 4       chi2     (2866.53635858, -1337303.60291, 468.141397755)  818123\n",
       " 5   dweibull      (1.02915052065, 2608.45578391, 2426.74728092)  679929\n",
       " 6       beta  (1.01077115558, 784406.572265, 0.97367595046, ...  658226\n",
       " 7    lognorm                (6.27614766846, 1.0, 8.40642380142)  771703\n",
       " 8      gamma      (225.36882514, -45524.5371733, 217.691648545)  684660\n",
       " 9   skewnorm     (245801934.959, 0.999900954465, 5004.91390844)  663431\n",
       " 10         f  (2.15899481033, 69.2541210189, -11.3562041693,...  658400\n",
       " 11  powerlaw               (0.266097686756, 1.0, 95117.0531482)  713320\n",
       " 12    pareto     (0.14788147075, -1.41375115185, 2.41375102757)  754921,\n",
       " <powerlaw.Fit at 0x111658080>)"
      ]
     },
     "execution_count": 50,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#total_mvps=cleaned_data.total_mvps.dropna()\n",
    "#total_mvps=total_mvps[total_mvps!= max(total_mvps)] # need to delete too extreme values again \n",
    "pipeline_(total_mvps)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "default_view": {},
   "name": "pipeline_analysis.ipynb",
   "provenance": [],
   "version": "0.3.2",
   "views": {}
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}