2018/day25_CLV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What’s a Customer Worth?\n",
    "\n",
    "[Source](http://mktg.uni-svishtov.bg/ivm/resources/Counting_Your_Customers.pdf) \n",
    "\n",
    "In E-Commerce or retail business, the relationship between businesses and customers are non-contractual relationship. In the non-contractual world, customers do go away, but they do so silently. \n",
    "\n",
    "We have to look at the time since a customer’s last transaction and ask a question: is the customer alive but dormant, or is the customer “dead” (“alive” means customers interact with us, “die” means they become inactive as customers)?\n",
    "\n",
    "**So, here we are: modelling customer lifetime value for non-contractual business.**\n",
    "\n",
    "## The data \n",
    "The data is  Online retail dataset from UCI Machine Learning Repository."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>536365</td>\n",
       "      <td>85123A</td>\n",
       "      <td>WHITE HANGING HEART T-LIGHT HOLDER</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "          InvoiceDate  UnitPrice  CustomerID         Country  \n",
       "0 2010-12-01 08:26:00       2.55     17850.0  United Kingdom  \n",
       "1 2010-12-01 08:26:00       3.39     17850.0  United Kingdom  \n",
       "2 2010-12-01 08:26:00       2.75     17850.0  United Kingdom  \n",
       "3 2010-12-01 08:26:00       3.39     17850.0  United Kingdom  \n",
       "4 2010-12-01 08:26:00       3.39     17850.0  United Kingdom  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel(\"data/Online Retail.xlsx\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   CustomerID InvoiceDate  Sales\n",
      "0     17850.0  2010-12-01  15.30\n",
      "1     17850.0  2010-12-01  20.34\n",
      "2     17850.0  2010-12-01  22.00\n",
      "3     17850.0  2010-12-01  20.34\n",
      "4     17850.0  2010-12-01  20.34\n",
      "4339\n"
     ]
    }
   ],
   "source": [
    "import datetime as dt\n",
    "\n",
    "df['InvoiceDate'] = pd.to_datetime(df['InvoiceDate']).dt.date\n",
    "df = df[pd.notnull(df['CustomerID'])]\n",
    "df = df[(df['Quantity']>0)]\n",
    "df['Sales'] = df['Quantity'] * df['UnitPrice']\n",
    "\n",
    "cols_of_interest = ['CustomerID', 'InvoiceDate', 'Sales']\n",
    "df = df[cols_of_interest]\n",
    "\n",
    "print(df.head())\n",
    "print(df['CustomerID'].nunique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2010-12-01\n",
      "2011-12-09\n"
     ]
    }
   ],
   "source": [
    "print(df.InvoiceDate.min())\n",
    "print(df.InvoiceDate.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 397924 entries, 0 to 541908\n",
      "Data columns (total 3 columns):\n",
      "CustomerID     397924 non-null float64\n",
      "InvoiceDate    397924 non-null object\n",
      "Sales          397924 non-null float64\n",
      "dtypes: float64(2), object(1)\n",
      "memory usage: 12.1+ MB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CLV Model Definition\n",
    "\n",
    "* Frequency represents the number of repeat purchases the customer has made. This means that it’s one less than the total number of purchases.\n",
    "* T represents the age of the customer in whatever time units chosen (daily, in our dataset). This is equal to the duration between a customer’s first purchase and the end of the period under study.\n",
    "* Recency represents the age of the customer when they made their most recent purchases. This is equal to the duration between a customer’s first purchase and their latest purchase. (Thus if they have made only 1 purchase, the recency is 0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CustomerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>12346.0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>325.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12347.0</th>\n",
       "      <td>6.0</td>\n",
       "      <td>365.0</td>\n",
       "      <td>367.0</td>\n",
       "      <td>599.701667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12348.0</th>\n",
       "      <td>3.0</td>\n",
       "      <td>283.0</td>\n",
       "      <td>358.0</td>\n",
       "      <td>301.480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12349.0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12350.0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>310.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            frequency  recency      T  monetary_value\n",
       "CustomerID                                           \n",
       "12346.0           0.0      0.0  325.0        0.000000\n",
       "12347.0           6.0    365.0  367.0      599.701667\n",
       "12348.0           3.0    283.0  358.0      301.480000\n",
       "12349.0           0.0      0.0   18.0        0.000000\n",
       "12350.0           0.0      0.0  310.0        0.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lifetimes.plotting import *\n",
    "from lifetimes.utils import *\n",
    "from lifetimes.estimation import *\n",
    "\n",
    "data = summary_data_from_transaction_data(df, 'CustomerID', 'InvoiceDate', monetary_value_col='Sales', observation_period_end='2011-12-9')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Float64Index: 4339 entries, 12346.0 to 18287.0\n",
      "Data columns (total 4 columns):\n",
      "frequency         4339 non-null float64\n",
      "recency           4339 non-null float64\n",
      "T                 4339 non-null float64\n",
      "monetary_value    4339 non-null float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 169.5 KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 4339 customers under our analysis.\n",
    "\n",
    "CustomerID 12346 made 1 purchase only (no repeat), so his frequency and recency are 0, and his age is 325 days (e.g. the duration between his first purchase and the end of the period in the analysis)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    4339.000000\n",
      "mean        2.864024\n",
      "std         5.952745\n",
      "min         0.000000\n",
      "25%         0.000000\n",
      "50%         1.000000\n",
      "75%         3.000000\n",
      "max       131.000000\n",
      "Name: frequency, dtype: float64\n",
      "0.3569946992394561\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(data['frequency'].describe())\n",
    "print(sum(data['frequency'] == 0)/float(len(data)))\n",
    "data['frequency'].plot(kind='hist', bins=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frequency/Recency Analysis Using the BG/NBD Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.BetaGeoFitter: fitted with 4339 subjects, a: 0.00, alpha: 68.91, b: 2.83, r: 0.83>\n"
     ]
    }
   ],
   "source": [
    "from lifetimes import BetaGeoFitter\n",
    "bgf = BetaGeoFitter(penalizer_coef=0.0)\n",
    "bgf.fit(data['frequency'], data['recency'], data['T'])\n",
    "print(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing our frequency/recency matrix\n",
    "\n",
    "Consider: a customer has made purchase every day for four weeks straight, and then we haven’t heard from him in months. What are the chances he is still “alive”? Pretty small, right? On the other hand, a customer who historically made purchase once a quarter, and again last quarter, is likely still alive. We can visualize this relationship using the frequency/recency matrix, which computes the expected number of transactions an artificial customer is to make in the next time period, given his recency (age at last purchase) and frequency (the number of repeat transactions he has made)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12e0e16a0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_frequency_recency_matrix\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "plot_frequency_recency_matrix(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a customer has made 120 purchases, and his latest purchase was when he was approximately 350 days old (i.e. Recency: the duration between her first transaction and her latest transaction is 350 days), then he is our best customer (bottom-right).\n",
    "\n",
    "Customers who have purchased a lot and purchased recently will likely be the best customers in the future. We will never have enough of them.\n",
    "\n",
    "Customers who have purchased a lot but not recently (top-right corner), have probably gone.\n",
    "\n",
    "There are also another type of customers that around (40, 300) that represents the customer who buys infrequently, and we have not seen him recently, so he might buy again. However, we are not sure if he has gone or just between purchases.\n",
    "\n",
    "We can predict which customers are surely alive:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12bb89e48>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_probability_alive_matrix\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "plot_probability_alive_matrix(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Customers who have purchased recently are almost surely “alive”.\n",
    "\n",
    "Customers who have purchased a lot but not recently, are likely to have dropped out. And the more they bought in the past, the more likely they have dropped out. They are represented in the upper-right.\n",
    "\n",
    "We are ranking customers from “highest expected purchases in the next period” to lowest. Models expose a method that will predict a customer’s expected purchases in the next period using their history."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "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>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "      <th>predicted_purchases</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CustomerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14606.0</th>\n",
       "      <td>88.0</td>\n",
       "      <td>372.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>135.890114</td>\n",
       "      <td>0.201001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15311.0</th>\n",
       "      <td>89.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>677.729438</td>\n",
       "      <td>0.203265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17841.0</th>\n",
       "      <td>111.0</td>\n",
       "      <td>372.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>364.452162</td>\n",
       "      <td>0.253048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12748.0</th>\n",
       "      <td>113.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>298.360885</td>\n",
       "      <td>0.257575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14911.0</th>\n",
       "      <td>131.0</td>\n",
       "      <td>372.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>1093.661679</td>\n",
       "      <td>0.298306</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            frequency  recency      T  monetary_value  predicted_purchases\n",
       "CustomerID                                                                \n",
       "14606.0          88.0    372.0  373.0      135.890114             0.201001\n",
       "15311.0          89.0    373.0  373.0      677.729438             0.203265\n",
       "17841.0         111.0    372.0  373.0      364.452162             0.253048\n",
       "12748.0         113.0    373.0  373.0      298.360885             0.257575\n",
       "14911.0         131.0    372.0  373.0     1093.661679             0.298306"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 1\n",
    "data['predicted_purchases'] = bgf.conditional_expected_number_of_purchases_up_to_time(t, data['frequency'], data['recency'], data['T'])\n",
    "data.sort_values(by='predicted_purchases').tail(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Listed above are our top 5 customers that the model expects them to make purchases in the next day. The predicted_purchases column represents their expected number of purchases while the other three columns represent their current RF metrics. The BG/NBD model believes these individuals will be making more purchases within the near future as they are our current best customers.\n",
    "\n",
    "### Assessing model fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12aa3fa90>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_period_transactions\n",
    "plot_period_transactions(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad, out model does not suck. So, we can continue on with our analysis.\n",
    "\n",
    "We now partition the dataset into a calibration period dataset and a holdout dataset. This is important as we want to test how our model performs on data not yet seen (just like cross-validation in machine learning practice)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            frequency_cal  recency_cal  T_cal  frequency_holdout  \\\n",
      "CustomerID                                                         \n",
      "12346.0               0.0          0.0  141.0                0.0   \n",
      "12347.0               2.0        121.0  183.0                4.0   \n",
      "12348.0               2.0        110.0  174.0                1.0   \n",
      "12350.0               0.0          0.0  126.0                0.0   \n",
      "12352.0               3.0         34.0  112.0                3.0   \n",
      "\n",
      "            duration_holdout  \n",
      "CustomerID                    \n",
      "12346.0                  184  \n",
      "12347.0                  184  \n",
      "12348.0                  184  \n",
      "12350.0                  184  \n",
      "12352.0                  184  \n"
     ]
    }
   ],
   "source": [
    "from lifetimes.utils import calibration_and_holdout_data\n",
    "summary_cal_holdout = calibration_and_holdout_data(df, 'CustomerID', 'InvoiceDate',\n",
    "                                        calibration_period_end='2011-06-08',\n",
    "                                        observation_period_end='2011-12-9' )   \n",
    "print(summary_cal_holdout.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_calibration_purchases_vs_holdout_purchases\n",
    "bgf.fit(summary_cal_holdout['frequency_cal'], summary_cal_holdout['recency_cal'], summary_cal_holdout['T_cal'])\n",
    "plot_calibration_purchases_vs_holdout_purchases(bgf, summary_cal_holdout);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this plot, we separate the data into both a in-sample (calibration) and validation (holdout) period. The sample period consists the beginning to 2011–06–08; the validation period spans from 2011–06–09 to 2011–12–09. The plot groups all customers in the calibration period by their number of repeat purchases (x-axis) and then averages over their repeat purchases in the holdout period (y-axis). The green and blue line presents the model prediction and actual result of the y-axis respectively. As we can see, our model is able to very accurately predict the customer base’s behaviour out of the sample, the model under-estimates at 4 purchases and after 5 purchases.\n",
    "\n",
    "## Customer transactions predictions\n",
    "Based on customer history, we can now predict what an individual’s future purchases might look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1572774135284996"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 10\n",
    "individual = data.loc[12347]\n",
    "bgf.predict(t, individual['frequency'], individual['recency'], individual['T'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "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>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "      <th>predicted_purchases</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CustomerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>12347</th>\n",
       "      <td>6.0</td>\n",
       "      <td>365.0</td>\n",
       "      <td>367.0</td>\n",
       "      <td>599.701667</td>\n",
       "      <td>0.015657</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            frequency  recency      T  monetary_value  predicted_purchases\n",
       "CustomerID                                                                \n",
       "12347             6.0    365.0  367.0      599.701667             0.015657"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc[[12347]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model predicts that customer 12347’s future transaction is 0.157 in 10 days."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Customer probability histories\n",
    "Given a customer transaction history, we can calculate their historical probability of being alive, according to our trained model. For example, we want to look at our best customer’s transactions history and see the probability of being alive:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oAxaFEE4HlsYYbwghvBpYHEIYBn4EfDfHsUiSJEm5yq2xjjEOA+/c7NsPjrn9XODcVp9v6IW7ZTQybYtzLbAOysY8i8MsVDTWZLOhF+7W8VIQN4hR18q65qyszCtt5pc280ub+aVtIjaIyXONtSRJklQZyTTWk2/8514PoTIm3/jPzresg5Ixz+IwCxWNNdmsm7lIZinI0Jy5IyuWPNDrYVTC7PnzAGh1vv2nsbS0fLmhNutAE6Pjy+2ZZyHU6zWG5swFzCJFZT3eVeX9oZ3j38DyZS4FkSRJknrFxlqSJEnKgI21JEmSlAEba0mSJCkDNtaSJElSBvLc0jxTK2/+fq+HUBnOtcA6KBvzLA6zUNFYk81W3vx9du7wsck01iPPelavh1AZzrXAOigb8ywOs1DRWJPNupmPZJaC9P3ud70eQmX0/e53zresg5Ixz+IwCxWNNdmsm7lI5oz1rCNeVfoLlxfFrCNeBZT/QvEan3VQLuZZHGahorEmm8064lWwfFlHj03mjLUkSZJUZDbWkiRJUgZsrCVJkqQM2FhLkiRJGbCxliRJkjKQzFVB1p53fq+HUBnOtcA6KBvzLA6zUNFYk83Wnnc+Mzp8bN/IyEimg8nL4OCaNAZaQfV6jcHBNb0ehlpkXmkzv7SZX9rML23t5Fev1/o6eQ2XgkiSJEkZSKaxnvGmo3s9hMqY8aajnW9ZByVjnsVhFioaa7JZN3ORzBrrgf9a2ushVIZzLbAOysY8i8MsVDTWZLNu5iOZM9aSJElSkdlYS5IkSRmwsZYkSZIyYGMtSZIkZSCZDy+uP/yIXg+hMpxrgXVQNuZZHGahorEmm60//AimdfhYN4hR17xgflrMK23mlzbzS5v5pc0NYiRJkqREJNNYT7vkgl4PoTKmXXKB8y3roGTMszjMQkVjTTbrZi6SWQoyNGfuyIolD/R6GJUwe/48AFqdb/9pLC2t5tVuHWhidPr7Zp7FUK/XGJozFzCLFJX1eFeV94d2jn8Dy5e5FESSJEnqFRtrSZIkKQM21pIkSVIGcruOdQihH7gc2AtYD5wQY1w6etvewKVj7r4/cHSM8Za8xiNJkiTlKc8NYo4GpsYYF4QQ9gcuBo4CiDH+K/BKgBDCHwO/2VZTPTJ9Ro5D1VjOtcA6KBvzLA6zUNFYk826mY88G+sDgVsAYoyLQwj7bn6HEMIOwAeBP9zWk628/a7MB6gtc64F1kHZmGdxmIWKxppstvL2u6h3+Ng8G+vpwOoxXw+FECbFGDeO+d47gH+MMT6yrSebNWsakyYNZD1GZaRer/V6CGqDeaXN/NJmfmkzv7TlnV+ejfVjwNjR92/WVAMcBxzbypOtvem7PLXggKzGpnFsd3fjb66tzndZr+tZVq3m1W4daGJ0+vtmnsVQr9dYdUNj5aNZpKesx7uqvD+0c/yb+frXdPQaeTbWdwELgWtH11jfP/bGEMIMYEqM8VetPFnt1JNLf+HyoqidejJQ/gvFa3zWQbmYZ3GYhYrGmmxWO/VkeP2yjh6bZ2N9HXBoCOHHQB+wKIRwOrA0xngD8CLgoRxfX5IkSZowuTXWMcZh4J2bffvBMbffQ+PKIZIkSVLy3CBGkiRJyoCNtSRJkpQBG2tJkiQpA3l+eDFTq6/+h14PoTKca4F1UDbmWRxmoaKxJputvvofmN3hY5NprIf+4KW9HkJlONcC66BszLM4zEJFY00262Y+XAoiSZIkZSCZxnr2/Hm9HkJlzJ4/z/mWdVAy5lkcZqGisSabdTMXyTTWkiRJUpHZWEuSJEkZsLGWJEmSMmBjLUmSJGXAxlqSJEnKQDLXsV73rvf0egiV4VwLrIOyMc/iMAsVjTXZbN273kOtw8f2jYyMZDqYvAwOrkljoBVUr9cYHFzT62GoReaVNvNLm/mlzfzS1k5+9Xqtr5PXcCmIJEmSlIFkGuvau07s9RAqo/auE51vWQclY57FYRYqGmuyWTdzkcwa6+3+5e5eD6EynGuBdVA25lkcZqGisSabdTMfyZyxliRJkorMxlqSJEnKgI21JEmSlAEba0mSJCkDyXx48an5+/Z6CJXhXAusg7Ixz+IwCxWNNdnsqfn7MtDhY90gRl3zgvlpMa+0mV/azC9t5pc2N4iRJEmSEpFMYz316qt6PYTKmHr1Vc63rIOSMc/iMAsVjTXZrJu5SGYpyNCcuSMrljzQ62FUwuz58wBodb79p7G0tJpXu3WgidHp75t5FkO9XmNozlzALFJU1uNdVd4f2jn+DSxf5lIQSZIkqVdsrCVJkqQM2FhLkiRJGbCxliRJkjJgYy1JkiRlIJmdF1fcfV+vh1AZzrXAOigb8ywOs1DRWJPNVtx9H/UOH5tMY83kyb0eQXU41wLroGzMszjMQkVjTTbrYj6SWQoy8J//0eshVMbAf/6H8y3roGTMszjMQkVjTTbrZi6SOWM9481vKP2Fy4tixpvfAJT/QvEan3VQLuZZHGahorEmm8148xtg+bKOHpvMGWtJkiSpyHI7Yx1C6AcuB/YC1gMnxBiXjrn9CODc0S/vA94dY0xjf3VJkiRpM3mesT4amBpjXAB8ALh40w0hhBpwIXBkjHF/4CFg5xzHIkmSJOUqz8b6QOAWgBjjYmDfMbe9ArgfuDiEcCfw2xjjYI5jkSRJknKV54cXpwOrx3w9FEKYFGPcSOPs9CHA3sBa4M4Qwt0xxq1+DLO/v496vZbjcPW0/j6AtubbbNLSUl4d1IEmRkeZmGdhDJhF0kqZW4Vqsp3jXyfybKwfA8aOvn+0qQZ4FLgnxvg/ACGEH9JosrfaWK++6NM8Nbgmr7FqjO0u+jRAy/Ndr9cYNJtktJpXu3WgidHp75t5FkO9XmOVWSSrrMe7qrw/tHP8m9nha+TZWN8FLASuDSHsT2PpxyZLgHkhhJ2BVcD+wBfHe7KnDj4kr3FqM861wDooG/MsDrNQ0ViTzbqZjzwb6+uAQ0MIPwb6gEUhhNOBpTHGG0IIZwG3jt732hijF0+UJElSsvpGRtK4wt1T+8wfWXXrD3o9jEqYefgrAWh1vsv6T2Nl1Wpe7daBJkanv2/mWQz1eo2n9pkPmEWKynq8q8r7QzvHv+3uW9LRQutkdl7sf+SRXg+hMpxrgXVQNuZZHGahorEmm3UzH+68KEmSJGXAxlqSJEnKgI21JEmSlAEba0mSJCkDyXx48ck3vaXXQ6gM51pgHZSNeRaHWahorMlmT77pLezQ4WOTudze4OCaNAZaQWW9/FBZmVfazC9t5pc280tbO/nV67WOLrfnUhBJkiQpA8k01juc+9e9HkJl7HDuXzvfsg5KxjyLwyxUNNZks27mIpnGesq3r+/1ECpjyrevd75lHZSMeRaHWahorMlm3cxFMo21JEmSVGQ21pIkSVIGbKwlSZKkDNhYS5IkSRlIZoOYoTlzez2EynCuBdZB2ZhncZiFisaabDY0Zy4DHT7WDWLUNS+YnxbzSpv5pc380mZ+aXODGEmSJCkRyTTWk2/+Tq+HUBmTb/6O8y3roGTMszjMQkVjTTbrZi6SWQoyNGfuyIolD/R6GJUwe/48AFqdb/9pLC2t5tVuHWhidPr7Zp7FUK/Xnl7PahbpKevxrirvD+0c/waWL3MpiCRJktQrNtaSJElSBmysJUmSpAzYWEuSJEkZaHmDmBDCZOBMIACnAqcBH48xbshpbJIkSVIy2tl58bPAILAPsBHYDbgS+NMcxvUMq268dSJeRjjXarAOysU8i8MsVDTWZLNVN97KTh0+tp3Gen6McZ8QwhExxnUhhD8H7u/wdds2vMtzJ+qlKs+5FlgHZWOexWEWKhprslk389HOGuuR0eUgmy58vfOYP+eub9XKiXqpyutbtdL5lnVQMuZZHGahorEmm3UzF+001p8C/i/w7BDCpcC9wCc7fuU2zfqjgybqpSpv1h8d5HzLOigZ8ywOs1DRWJPNupmLlpeCxBi/FkK4FzgEGAAWxhj/reNXliRJkkqknauC/CtwNfD1GOP/y29IkiRJUnra+fDiccBbgDtCCMuAvwO+GWNcm8vIJEmSpIS0vMY6xvjvMca/iTG+CPgQ8B7gt7mNTJIkSUpIO0tBBoDDgTcDBwO30tgkRpIkSaq8dpaC/BpYDFwDnDDROy4+fvY5E/lyleZcC6yDsjHP4jALFY012ezxs89heoeP7RsZae1S1CGE2THGFR2+TtcGB9dM2DWz1Z56vcbg4JpeD0MtMq+0mV/azC9t5pe2dvKr12t9nbzGNs9YhxC+HWM8ElgSQhjb3PYBIzHGF2zlcf3A5cBewHoaZ7mXjrn908ABwKaf8KgY4+pOfghJkiSp11pZCnLi6P9f2eZzHw1MjTEuCCHsD1wMHDXm9n2Aw2OMj7TyZNOP+2Meu+Yf2xyCOjH9uD8GcL4rzjooF/MsDrNQ0ViTzaYf98dw2y0dPbaVxvrQEMJ4t39tK98/ELgFIMa4OISw76YbRs9m7w58IYTwe8CXY4xXjjvQB3/RwlCVBedaYB2UjXkWh1moaKzJZt3MRyuN9SHj3DbC1hvr6cDYpR1DIYRJMcaNwA7AZ4BLaOzieHsI4d7xdnLs7++jXq+1MFx1rb+xrKid+TabtLSUVwd1oInRUSbmWRgDZpG0UuZWoZps5/jXiW021jHGRVu7LYSw/TgPfQwYO/r+0aYaYB3wqRjjutHn+T6NtdhbbayHh0dY4QcGJsTs4cZS+lbn2w9zpKXVvNqtA02MTn/fzLMY6vUaQ2aRrLIe76ry/tDO8W+gw9do5zrWC4HzgR1pfHBxANgeeNZWHnIXsBC4dnSN9f1jbnsR8I0Qwj40Nqk5EPhq26OXJEmSCqKd61h/ksYHGf8K+AiNDyfuMM79r6OxPvvHNBrxRSGE04GlMcYbQgjX0Lgu9lPA12KM/97JDyBJkiQVQTuN9aoY4+0hhAOAGTHG94cQfr61O8cYh4F3bvbtB8fcfgFwQasvvuGQV7cxVHXDuRZYB2VjnsVhFioaa7LZhkNezXhrncfTzgYxdwLvAPYA9gPOAX4eY9ytw9duixvEFFdZ15yVlXmlzfzSZn5pM7+0TcQGMf1t3PdvaKyx/jbwR8BvgX/u5EUlSZKksmm5sY4x3hFjfFOMcX2McT/gBTHGMwBCCOflNcBNtv/MpXm/hEZt/5lLnW9ZByVjnsVhFioaa7JZN3PR8lKQ8YQQ7osx7tP1E41jaM7ckRVLHsjzJTRq9vx5ALQ63/7TWFpavtxQm3WgidHx5fbMsxDq9RpDc+YCZpGish7vqvL+0M7xb2D5styXgoyn8ytpS5IkSSWQVWPtBwslSZJUaVk11pIkSVKl2VhLkiRJGdjmBjEhhF2Ai4CXAncDH4gxrtrsblvdKCYrI9Om5f0SGuVcC6yDsjHP4jALFY012ayb+djmVUFCCLcC9wO3A8cCxBgXdfyKHXKDmOIq66eky8q80mZ+aTO/tJlf2iZig5hWtjR/bozxcIAQwm3Av3byQpIkSVKZtbLGesOmP8QYnxr79USadO9PevGylTTp3p8437IOSsY8i8MsVDTWZLNu5qKVM9ab68mSjOknv730Fy4viuknvx0o/4XiNT7roFzMszjMQkVjTTabfvLbYfmyjh7bSmP90hDCf4/5+rmjX/cBIzHGF3T0ypIkSVKJtNJYvyj3UUiSJEmJ22ZjHWPs7Fy4JEmSVCFuECNJkiRlwMZakiRJykAnVwXpiceuvLrXQ6gM51pgHZSNeRaHWahorMlmj115NbM6fGwyjfXGvf5Pr4dQGc61wDooG/MsDrNQ0ViTzbqZD5eCSJIkSRlIprGe9fK9ez2Eypj18r2db1kHJWOexWEWKhprslk3c5HMUpC+jRt7PYTKcK4F1kHZmGdxmIWKxpps1s18JHPGWpIkSSoyG2tJkiQpAzbWkiRJUgZsrCVJkqQMJPPhxSdOOqXXQ6gM51pgHZSNeRaHWahorMlmT5x0Cjt2+Ni+kZGRTAeTl8HBNWkMtILq9RqDg2t6PQy1yLzSZn5pM7+0mV/a2smvXq/1dfIaLgWRJEmSMpBMY73jae/u9RAqY8fT3u18yzooGfMsDrNQ0ViTzbqZi2TWWE++845eD6Fi/EXKAAAc+klEQVQynGuBdVA25lkcZqGisSabdTMfyZyxliRJkorMxlqSJEnKgI21JEmSlAEba0mSJCkDuX14MYTQD1wO7AWsB06IMS7dwn2+A1wfY7xivOfbuMdeeQ1Vm3GuBdZB2ZhncZiFisaabLZxj70Y6PCxeV4V5GhgaoxxQQhhf+Bi4KjN7nM+MLuVJ3vsqmsyHp62xrkWWAdlY57FYRYqGmuy2WNXXUO9w8fmuRTkQOAWgBjjYmDfsTeGEI4FhoGbcxyDJEmSNCHyPGM9HVg95uuhEMKkGOPGEMI84K3AscA5rTzZ7Bv+kYF3vD2HYeoZrrqq8f/jj2/5IfV6LZehKB8t5dVBHWhidPT7Zp6FUf/ONxt/MIsklfJ4V6H3h5aPfx3ORd/IyEhHD9yWEMIlwOIY47WjX/86xvi80T9fABwMPAHsCmwA3hNjvGVrzzc0Z+7IiiUP5DJWNZs9fx4Arc53vV5jcHBNnkNShlrNq9060MTo9PfNPIuhXq8xNGcuYBYpKuvxrirvD+0c/waWL+vr5DXyPGN9F7AQuHZ0jfX9m26IMb5v059DCOcB/zNeUy1JkiQVXZ6N9XXAoSGEHwN9wKIQwunA0hjjDTm+riRJkjThcmusY4zDwDs3+/aDW7jfeXmNQZIkSZoobhAjSZIkZcDGWpIkScpAnmusM7XijsW9HkJlONcC66BszLM4zEJFY002W3HH4o43iEmmsWbHHXs9gupwrgXWQdmYZ3GYhYrGmmzWxXwksxSk/6Ff9noIldH/0C+db1kHJWOexWEWKhprslk3c5HMGeuZb1xY+guXF8XMNy4Eyn+heI3POigX8ywOs1DRWJPNZr5xISxf1tFjkzljLUmSJBWZjbUkSZKUARtrSZIkKQM21pIkSVIGbKwlSZKkDCRzVZC1F1zS6yFUhnMtsA7KxjyLwyxUNNZks7UXXMKMDh/bNzIykulg8jI4uCaNgVZQvV5jcHBNr4ehFplX2swvbeaXNvNLWzv51eu1vk5ew6UgkiRJUgaSaaxnHnlYr4dQGTOPPMz5lnVQMuZZHGahorEmm3UzF8msse7/f7/p9RAqw7kWWAdlY57FYRYqGmuyWTfzkcwZa0mSJKnIbKwlSZKkDNhYS5IkSRmwsZYkSZIykMyHF9cfc2yvh1AZzrXAOigb8ywOs1DRWJPN1h9zLNM6fKwbxKhrXjA/LeaVNvNLm/mlzfzS5gYxkiRJUiKSaax3OP+8Xg+hMnY4/zznW9ZByZhncZiFisaabNbNXCSzFGRoztyRFUse6PUwKmH2/HkAtDrf/tNYWlrNq9060MTo9PfNPIuhXq8xNGcuYBYpKuvxrirvD+0c/waWL3MpiCRJktQrNtaSJElSBmysJUmSpAzYWEuSJEkZSGaDmOHn7NLrIVSGcy2wDsrGPIvDLFQ01mSz4efswkCHj03mqiBuEFNcZf2UdFmZV9rML23mlzbzS5sbxEiSJEmJSKaxnvy923o9hMqY/L3bnG9ZByVjnsVhFioaa7JZN3ORzFIQN4iZOG4QU25uEJM2N4hJmxvEpK2sx7uqvD+4QYwkSZKUiNyuChJC6AcuB/YC1gMnxBiXjrn93cDxwAjwoRjjt/MaiyRJkpS3PM9YHw1MjTEuAD4AXLzphhDCzsC7gFcAfwR8LoTQ0Sl3SZIkqQjybKwPBG4BiDEuBvbddEOM8RFgrxjjU8CzgVUxxjQWe0uSJElbkOcGMdOB1WO+HgohTIoxbgSIMW4MIZwKfBD49LaerL+/j3q9ls9I1ay/8Y8H7cy32aSlpbw6qANNjI4yMc/CGDCLpJUytwrVZDvHv07kdlWQEMIlwOIY47WjX/86xvi8LdxvMnAzcH6M8fatPd+j9/zbyPCuz89lrGrW/9AvAWh1vsv6KemyajWvdutAE6PT3zfzLIZ6vcaj9/wbYBYpKuvxrirvD+0c/3bab8+Ouus8z1jfBSwErg0h7A/cv+mGEEIAPga8EXiKxocbh8d7srKHXSTOtcA6KBvzLA6zUNFYk826mY88G+vrgENDCD8G+oBFIYTTgaUxxhtCCD8D7qZxVZCbY4x3jPtsa9fCjjvmOFw9be3axv+d72qzDsrFPIvDLFQ01mSztWuhw2UxbhCjZ3CDmHJzg5i0uUFM2twgJm1lPd5V5f3BDWIkSZKkRNhYS5IkSRmwsZYkSZIyYGMtSZIkZcDGWpIkScpAnpfby9TjZ57V6yFUhnMtsA7KxjyLwyxUNNZks8fPPIvpHT42mcvtDQ6uSWOgFVTWyw+VlXmlzfzSZn5pM7+0tZNfvV7zcnuSJElSryTTWE8//rheD6Eyph9/nPMt66BkzLM4zEJFY00262YuklljPen+n/V6CJXhXAusg7Ixz+IwCxWNNdmsm/lI5oy1JEmSVGQ21pIkSVIGbKwlSZKkDNhYS5IkSRlI5sOLGw46uNdDqAznWmAdlI15FodZqGisyWYbDjqY7Tt8rBvEqGteMD8t5pU280ub+aXN/NLmBjGSJElSIpJprLf//Gd7PYTK2P7zn3W+ZR2UjHkWh1moaKzJZt3MRTJLQYbmzB1ZseSBXg+jEmbPnwdAq/PtP42lpdW82q0DTYxOf9/Msxjq9RpDc+YCZpGish7vqvL+0M7xb2D5MpeCSJIkSb1iYy1JkiRlwMZakiRJyoCNtSRJkpSBZDaIGZmUzFCT51wLrIOyMc/iMAsVjTXZrJv5SOaqIG4QU1xl/ZR0WZlX2swvbeaXNvNLmxvESJIkSYlIprGe9LOf9noIlTHpZz91vmUdlIx5FodZqGisyWbdzEUyS0HcIGbiuEFMublBTNrcICZtbhCTtrIe76ry/uAGMZIkSVIibKwlSZKkDNhYS5IkSRmwsZYkSZIyYGMtSZIkZSCZrXYe+/yVvR5CZTjXAuugbMyzOMxCRWNNNnvs81cyq8PHJtNYb9z3Zb0eQmU41wLroGzMszjMQkVjTTbrZj5cCiJJkiRlILcz1iGEfuByYC9gPXBCjHHpmNv/Enjz6Jc3xRg/ON7zzTroZay88yd5DVdjzDqo8Tc157varINyMc/iMAsVjTXZbNZBL4MHf9HRY/M8Y300MDXGuAD4AHDxphtCCC8AjgNeASwADgsh7Dnek/WtW5fjUDVW37p1zresg5Ixz+IwCxWNNdmsm7nIs7E+ELgFIMa4GNh3zG2/Al4TYxyKMQ4D2wFP5jgWSZIkKVd5fnhxOrB6zNdDIYRJMcaNMcangEdCCH3AhcBPY4z/Md6T9ff3Ua/XchyuntbfB9DWfJtNWlrKq4M60MToKBPzLIwBs0haKXOrUE22c/zrRJ6N9WPA2NH3xxg3bvoihDAVuBJYA7xrW082PDzCisE1mQ9SzzR7eASg5fmu12sMmk0yWs2r3TrQxOj09808i6FerzFkFskq6/GuKu8P7Rz/Bjp8jTyXgtwFvBYghLA/cP+mG0bPVF8P/CzGeHKMcSjHcUiSJEm5y/OM9XXAoSGEHwN9wKIQwunAUmAAOBiYEkI4YvT+Z8UY797akz1x/Ak5DlVjOdcC66BszLM4zEJFY002e+L4E9ixw8f2jYyMZDqYvAwOrkljoBVU1n8aKyvzSpv5pc380mZ+aWsnv3q91tFCazeIkSRJkjKQTGO94xmn9XoIlbHjGac537IOSsY8i8MsVDTWZLNu5iLPNdaZmnz7/+31ECrDuRZYB2VjnsVhFioaa7JZN/ORzBlrSZIkqchsrCVJkqQM2FhLkiRJGbCxliRJkjKQzIcXN774Jb0eQmU41wLroGzMszjMQkVjTTbb+OKXdLyluRvEqGteMD8t5pU280ub+aXN/NLmBjGSJElSIpJprKd889peD6EypnzzWudb1kHJmGdxmIWKxpps1s1cJLMUZGjO3JEVSx7o9TAqYfb8eQC0Ot/+01haWs2r3TrQxOj09808i6FerzE0Zy5gFikq6/GuKu8P7Rz/BpYvcymIJEmS1Cs21pIkSVIGbKwlSZKkDNhYS5IkSRmwsZYkSZIykMzOiyu/d2evh1AZzrXAOigb8ywOs1DRWJPNVn7vTnbu8LHJNNYjM2f1egiV4VwLrIOyMc/iMAsVjTXZrJv5SGYpSP9vHu71ECqj/zcPO9+yDkrGPIvDLFQ01mSzbuYimTPWMxceXvoLlxfFzIWHA+W/ULzGZx2Ui3kWh1moaKzJZjMXHg7Ll3X02GTOWEuSJElFZmMtSZIkZcDGWpIkScqAjbUkSZKUARtrSZIkKQPJXBVk7fmf6PUQKsO5FlgHZWOexWEWKhprstna8z/BjA4f2zcyMpLpYPIyOLgmjYFWUL1eY3BwTa+HoRaZV9rML23mlzbzS1s7+dXrtb5OXsOlIJIkSVIGkmmsZxzzul4PoTJmHPM651vWQcmYZ3GYhYrGmmzWzVwks8Z6oMMdcNQ+51pgHZSNeRaHWahorMlm3cxHMmesJUmSpCKzsZYkSZIyYGMtSZIkZcDGWpIkScpAbh9eDCH0A5cDewHrgRNijEs3u08d+DGwR4zxyfGeb/2RR+U1VG3GuRZYB2VjnsVhFioaa7LZ+iOPYlqHj81tg5gQwhuA18cYjw8h7A+cFWM8aszthwMfB14IPGtbjbUbxBSXF8xPi3mlzfzSZn5pM7+0pb5BzIHALQAxxsXAvpvdPgy8GliR4xgkSZKkCZHndaynA6vHfD0UQpgUY9wIEGP8LkAIoaUn2+nTF9D/4Q9nPkhtwbnnNv7/wQ+2/JB6vZbTYJSHlvLqoA40MTr6fTPPwqhfdlHjD2aRpFIe7yr0/tDy8a/DuchzKcglwOIY47WjX/86xvi8LdzvIeDF21oKMjRn7siKJQ/kMVRtZvb8eQC0Ot/+01haWs2r3TrQxOj09808i6FerzE0Zy5gFikq6/GuKu8P7Rz/BpYvK9xSkLuA1wKMrrG+P8fXkiRJknoqz6Ug1wGHhhB+DPQBi0IIpwNLY4w35Pi6kiRJ0oTLrbGOMQ4D79zs2w9u4X675jUGSZIkaaK4QYwkSZKUgTyXgmRqeOedez2EynCuBdZB2ZhncZiFisaabDa8884MdPjY3K4KkjU3iCmusn5KuqzMK23mlzbzS5v5pS31DWIkSZKkykimsd7ujtt7PYTK2O6O251vWQclY57FYRYqGmuyWTdzkcxSEDeImThuEFNubhCTNjeISZsbxKStrMe7qrw/pL5BjCRJklQZNtaSJElSBpK53F5R3XffvZxzzlnsuuvz6evrY/369Rx22Gs49tg3t/wcX/7y59lpp5146Uv34Ec/+iGLFp2Y44glSZKUh9I01td+fyn3PPi7TJ9zvxc/ize9ardt3m/+/H354Ac/BsCGDRt461vfyOGHv45ardbW6+2+e2D33UNHY5UkSVJvlaaxLop169bR39/PwMCWLy1+xRWX8eCDP2fdunXsuuvzOfvsc5++7b777uX667/JoYe+hh/+8AdP37Zo0Vu55JLL+OlP7+Mf/uEa+vv72XPPvTnllL+YkJ9JkiRJ25ZMY736G98a9/Y3vWq3ls4u52HJkns59dST6O/vZ9KkSfzlX57JtGnTnnG/xx9fS61W49JLL2d4eJi3ve1NDA4+8yz7ggUHcvnln+aJJ57goYf+m+c+93kMDAxw5ZWf50tfupqpU6fy4Q//Lffcs5j99ts/859nW3OtarAOysU8i8MsVDTWZLPV3/gWszt8bDKN9dDuL+r1ELZq7FKQ8UyZMpWVK1dy7rlnM23aNJ544gk2btz4jPsNDAzwylf+EXfc8X0eeOB+Fi48hl//+lesWrWSM854D9A4M/7www+z336Z/ziFnmtNHOugXMyzOMxCRWNNNutmPpJprNmwASZP7vUourJ48V387ne/5UMf+hgrV67khz+8na1dR/zII4/iwgs/yurVqzj99PexevVqnvWs3+PSSy9n0qRJ3HTTjeye1y/Chg2N/yc+3+qSdVAu5lkcZqGisSabbZqPDiTTWM9esE/yFy5/yUteylVXfZmTTjqeyZMns8suz+WRRwa3eN9ddnkuAAcd9Er6+/uZNWsWf/Inx3HqqScxNDTEc56zC6961aG5jHP2gn2A8l8oXuOzDsrFPIvDLFQ01mSz2Qv2geXLOnpsMo11Ue2zz77ss8++Ld13p5125ktf+tozvr/nnns3Pd8mn/zkZ5vud/jhr+Xww1/b4UglSZKUJxvrHFx//bf47ndvecb33/nOU5k3b88ejEiSJEl5s7HOwVFHvYGjjnpDr4chSZKkCeSW5pIkSVIGbKwlSZKkDCSzFGTdaWf0egiV4VwLrIOyMc/iMAsVjTXZbN1pZ1Dr8LF9W7uOctEMDq5JY6BdOPbYhVxzzT8xZcqUXg+lLfV6jcHBNb0ehlpkXmkzv7SZX9rML23t5Fev1/o6eQ2XgkiSJEkZSGYpSO2k41nzhavGvc/s+fO2+P1173oPT77jpMbzvOtEtvuXu59xn6fm7/v080+9+iqmXXpRSxdKv+mmG7nzzjtYt+5xVq1axaJFJ3DZZZc+feb5c5/7DHPn7sqzn/0cPve5z7Dddtvx+tcfQ602na985YsA7L574MwzzwLg4os/zm9+8zAAH/3oRQwM9PPxj5/P2rVrWL16FQsXHsMxxxzLt771j9x887fp7+9nzz335t3vfi+//e3/cMEFH2XDhvVMnjyF973vbGbOnMU553yAxx9/nPXrn+SUU96zzetu1046HmCb861ysw7KxTyLwyxUNNZks9pJx8N13+zosck01tstubfXQ9iqJ55Yxyc/+VlWrVrJiSf+OcPDw1u834YNG/jiF7/Kxo0befObj+GLX/wqs2bN5itf+SK/+93vAHjd645ir7325iMfOY977vkXnve83+fVrz6Mgw9+FY88Msipp57EMcccy0033chpp53JvHl7cN11/8TGjRv57Gc/xbHH/gkLFhzAvff+hCuuuIy3vW0RK1Y8yqWXXs7KlSv51a+2vZNQkedaE8c6KBfzLA6zUNFYk826mY9kGutWtHKGec3lX9zmfZ582/E8+bbjW37dvffeh/7+fmbP3olabTrLlv3y6dvGrmGfM2cuAKtXr6JWqzFr1mwAFi068en7vPjFLwZg9uydWL/+SXbaaSeuvfbr3HHH7UybtgMbN24E4Oyzz+Hv//7vuOKKz/DSl+4BwH//91KuvvorXHPNVwGYNGkSL3jBC3nDG97Eeef9NRs3buTYY9/c8s8lSZKk1pWqse6VGB8EYMWKR3n88cf5vd97No8++gjPec4uLF36H+y66/MB6O9vrIOfNWs2a9eu5bHHVjN9+gwuvfRCDjvsiNFna14r//d/fzXz5u3JMcccy3333cvdd/8IgBtu+GfOOOMspkyZwumnn8r99/+MOXN25S1v+VP22GMvli17iJ/+dAn/9V9LWbfucS688FM88sgjnHLK2znggIMmZmIkSZIqxMY6AytWPMp733sKa9eu5a/+6v088sggZ575Xp797F2o1Z55wZb+/n5OP/39nHnmafT39/OiFwVe8pKXbvG5DzjgD7nooo9x2203M2PGDAYGBtiwYQMvfOFunHjinzFz5izq9Tp/8AfzePe738vFF3+cDRs2sH79k7z3vWfwvOf9Pl/5yhe45ZbvMGnSdrzjHSfnPR2SJEmVlMzl9obmzB1pZanHRLvpphtZtuwhTjnlL3o9lMxs+hBoq/Pt5YfS0mpe7daBJkanv2/mWQz1eo2h0WWBZpGesh7vqvL+0M7xb2D5so4ut5fMGeunXr6g10OoDOdaYB2UjXkWh1moaKzJZk+9fAEDHT42mTPWVdggJlVl/Rt8WZlX2swvbeaXNvNLmxvESJIkSYlIprGe+uUv9HoIlTH1y19wvmUdlIx5FodZqGisyWbdzEUyS0GK+uHFMvLDi+XmhxfT5ocX0+aHF9NW1uNdVd4fJuLDi8mcsZYkSZKKzMZakiRJykBul9sLIfQDlwN7AeuBE2KMS8fcfiJwMrAROD/G+O28xiJJkiTlLc8z1kcDU2OMC4APABdvuiGE8GzgPcABwOHAx0IIU3IciyRJkpSrPBvrA4FbAGKMi4F9x9z2MuCuGOP6GONqYCmwZ45jkSRJknKV586L04HVY74eCiFMijFu3MJta4AZ4z3ZwPJlffXsx6gtWb4MgHbmu16v5TMW5aKlvDqoA02Mjn7fzLMwBswiaaU83lWoJts5/nUizzPWjwFjR98/2lRv6bYasCrHsUiSJEm5yrOxvgt4LUAIYX/g/jG3/QQ4KIQwNYQwA3gJUO6LJ0qSJKnUctsgZsxVQfYE+oBFNBrtpTHGG0avCnISjeb+ozHGb+YyEEmSJGkCJLPzoiRJklRkbhAjSZIkZcDGWpIkScpAnpfbU8GFELYDrgR2BaYA5wM/B64CRmh8oPTdMcbh0fvvBvxzjHHeZs9zGvDsGOMHtvAaOwNfB7YHfgMsijGuCyH8JfDm0bvdFGP8YOY/YMn0Mq/R2/qB7wDXxxivyOFHLLUe/74dAZw7erf7Rl/HdYBt6HF+ZwBvAYZpfCbpujx+xjKbiPy2dp8QwkLgHBo7TV8ZY/xipj9cyfU4u7cApwFDwL8B79r0OlvjGetq+1Pg0RjjQcARwGXAJcDfjH6vDzgKIITwNuAbwM6bHhxC2D6E8HfAu8d5jXOAr48+30+Bk0MILwCOA14BLAAOCyG4QdC29SSvMbedD8zO7sepnF79vtWAC4EjY4z7Aw+NfV61rFf5zaSxU/EC4DDg0qx/sIrIPb8t3We0KfwkjewOBk4a3X1aretVdtvTOO4dEmN8BY39Vo7c1mBtrKvtH4G/HfP1RmA+cMfo1zcDrx7980oabwpjTQW+BnxknNd4egfOMc/3K+A1Mcah0b/5bQc82eHPUCW9yosQwrE0zpbd3OHY1bv8XkHjcqcXhxDuBH4bYxzs8Geosl7l9ziwDNhh9L9xz5ZpqyYivy3d5yU0roa2Msa4AfgRcFAnP0CF9Sq79cArNv2rLY1VHtvsVWysKyzGuDbGuGb0jNY/AX8D9I35J+Knd8SMMX47xvj4Zo9fGWO8bRsvM3aXzTXAjBjjUzHGR0IIfSGEi4Cfxhj/I6ufq6x6lVcIYR7wVhpn09ShXuVH48zNIcD7aZztOS2E8KIsfqYq6WF+0DgZ8XMay3g+3fUPU0ETkd9W7tP2TtNq1qvsYozDMcbfAoQQ/gLYEfjutsZrY11xIYTfB24Hro4xfp3msyFt74gZQjgwhPCD0f9eR/Mum08/XwhhKnDN6Pfe1d1PUR09yuvPgOcC3weOB04PIbymqx+konqU36PAPTHG/4kxrgV+COzd5Y9SST3K7wjgOcDzgTnA0SGEl3X3k1TTBOS3Je40nYEeZUcIoX/0BOChwBtb+WyKH16ssBDC7wG3AafGGL83+u2fhhBeGWP8AY039Nvbec4Y44+AV455jdfQ2BjoqtHnuzOE0AdcD3w/xviJLn+MyuhVXmMzCiGcB/xPjPEW1JZe5QcsAeaNfjBuFbA/4Ien2tTD/FYCTwDrY4wjIYRVwMyufpgKmoj8tuIXwO4hhNnAWuAPgYvaeZ2q62F2AJ+nsSTk6G19aHETG+tqOxuYBfxtCGHT+qX3Ap8OIUym8YbwT12+xvnAV0Njp81HaCwpOJrGGqgpo1crADgrxnh3l69Vdr3KS9noSX4xxsdDCGcBt47e59oY4wNdvk4V9TK/VwOLQwjDNNbobvOfo/UME5HfM8QYnwohnE7j96+fxlVBHs76dUquJ9mFEPYB3kHjL7jfDyEAfGpbV+Vx50VJkiQpA66xliRJkjJgYy1JkiRlwMZakiRJyoCNtSRJkpQBG2tJkiQpAzbWkiRJUgZsrCVJkqQM2FhLkiRJGfj/2IpJRqAVIO0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_history_alive\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "id = 12347\n",
    "days_since_birth = 365\n",
    "sp_trans = df.loc[df['CustomerID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'InvoiceDate');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our best customer is definitely alive, however, he had several hiatus in the second half of the year 2011."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "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>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "      <th>predicted_purchases</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CustomerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14729</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.001871</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            frequency  recency      T  monetary_value  predicted_purchases\n",
       "CustomerID                                                                \n",
       "14729             0.0      0.0  373.0             0.0             0.001871"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc[[14729]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p4V/+ctsJJEmSpEqUU8IlSZKkHlFOCb/ssrYTSJIkSZUop4R/6ENtJ5AkSZIqUU4JlyRJknqEJVySJElqmCVckiRJapglXJIkSWqYJVySJElqWDkl/Be/aDuBJEmSVIlySvjGG7edQJIkSapEOSX8vvvaTiBJkiRVopwSvv/+bSeQJEmSKlFOCZckSZJ6xIS6Fo6IPuASYBdgMTAjM+d2bT8AOHPo4d3AcZm5oq48kiRJ0lhR55nwQ4CJmTkFOBW4YOWGiOgHzgPemJmTgfuBZ9WYRZIkSRoz6izhU4FZAJk5G9i9a9urgDnABRHxA+DBzBysMYskSZI0ZtR2OQqwGbCw6/GyiJiQmUvpnPXeC9gVeBj4QUTckZkjfhn4wEB/bWHVHOdYFudVNudXNudXNuenkdRZwh8Cun/7+oYKOMAfgTsz8/cAEXELnUK++hL+mc8wOLiopqhqysBAv3MsiPMqm/Mrm/Mrm/MrWxNvoOq8HOU24ECAiJhM5/KTlX4M7BgRz4qICcBk4Gcjrrb33jXFlCRJkppV55nwq4F9IuJ2YBwwPSJmAnMz89qIOA341tC+X8nMe2vMIkmSJI0ZtZXwzFwOHLPK0/d1bf8y8OVRL/iKV8A3v1dNOEmSJKlF5dys5w9/aDuBJEmSVIlySrgkSZLUIyzhkiRJUsMs4ZIkSVLDLOGSJElSw8op4e98Z9sJJEmSpEqUU8LPPrvtBJIkSVIlyinhkiRJUo8op4SffHLbCSRJkqRKlFPCv/rVthNIkiRJlSinhEuSJEk9whIuSZIkNcwSLkmSJDXMEi5JkiQ1rJwS/qIXtZ1AkiRJqkQ5Jfymm9pOIEmSJFWinBIuSZIk9YhySvg117SdQJIkSapEOSX8xBPbTiBJkiRVopwSLkmSJPUIS7gkSZLUMEu4JEmS1DBLuCRJktSwCaPdMSI2Bk4BAjgeOAn4SGYuqSmbJEmS1JPW5kz4xcDTgZcBS4EXA5fXEWpYt97a2KEkSZKkOq1NCd8tM08HnsjMR4F3ArvWE2sY22zT2KEkSZKkOq1NCV8xdEnKiqHHz+r6c/3mz2/sUJIkSVKd1qaEXwR8F9g6Ii4E7gI+Vkuq4fz1Xzd2KEmSJKlOo/5gZmZ+PiLuAvYCxgMHZeZ/1JZMkiRJ6lFr8+0oPwGuAr6Ymf+3vkiSJElSbxt1CQfeBhwO3BwRDwD/CnwtMx+uJZkkSZLUo0Z9TXhm/mdmfiAztwc+CJwAPFhbMkmSJKlHrc3lKOOB/YDDgNcA36Jzwx5JkiRJa2FtLkf5DTAb+AIwo/E7ZX74w40eTpIkSarL2pTwHTLzT7UlWZMjjoDBRa0dXpIkSarKGkt4RHwjM98I/Dgium/OMw5YkZnbrubn+oBLgF2AxXTOns/t2v5xYA9gZbM+ODMXrtvLkCRJksoxmjPhRw3972vXcu1DgImZOSUiJgMXAAd3bX8ZsF9mzhvVam98I1zxpbWMIEmSJI09oynh+0TESNs/v5rnpwKzADJzdkTsvnLD0Fny7YBPR8RzgM9m5uUjprj33lFElSRJksa+0ZTwvUbYtoLVl/DNgO7LS5ZFxITMXAo8HfgE8M907r55U0TctaY7cA4M9I8irsY651gW51U251c251c256eRrLGEZ+b01W2LiKeN8KMPAd2/fX1DBRzgUeCizHx0aJ0b6Vw7PmIJH/SDmcUbGOh3jgVxXmVzfmVzfmVzfmVr4g3U2nxP+EHAOcAz6HwoczzwNODZq/mR24CDgK8MXRM+p2vb9sCXI+JldG4YNBW4cq3TS5IkSQVam68o/BidD2n+A/AhOh+8fPoI+19N53ry2+mU9ukRMROYm5nXRsQX6Hzv+BPA5zPzP9flBUiSJEmlWZsSviAzb4qIPYDNM/N9EfGz1e2cmcuBY1Z5+r6u7R8FPjrqo++//1pElSRJksauvrXY97GI2B74OfDaiNgY2LieWMO49NLGDiVJkiTVaW1K+AfoXBP+DeD1wIPAv9cRSpIkSeploy7hmXlzZr41Mxdn5suBbTPzZICIOKuugH/20dFfuSJJkiSNZWtzJvxJMnN+18M3VZBlZJdcUvshJEmSpCascwlfxbiK1pEkSZJ6XlUlfEVF60iSJEk9r6oSLkmSJGmULOGSJElSw9Z4s56IeB5wPrADcAdwamYuWGW31d60pzJPH+nmnJIkSVI5RnMm/Argd8DpwCZ0bl//JJn5txXneqr/9K72kiRJ6g2juW398zNzP4CI+Dbwk3ojSZIkSb1tNGfCl6z8Q2Y+0f24UbNnt3JYSZIkqWrr8sHMdr6O8LDDWjmsJEmSVLXRXI6yQ0T8suvx84cejwNWZOa29USTJEmSetNoSvj2taeQJEmSNiBrLOGZ+UATQSRJkqQNhTfrkSRJkhpmCZckSZIaVk4J/9rX2k4gSZIkVaKcEr7bbm0nkCRJkipRTgmXJEmSekQ5JXy77dpOIEmSJFWinBL+xBNtJ5AkSZIqUU4JlyRJknqEJVySJElqmCVckiRJapglXJIkSWpYOSX8pJPaTiBJkiRVwhIuSZIkNaycEi5JkiT1iHJK+Lve1XYCSZIkqRLllPDvfa/tBJIkSVIlyinhkiRJUo+whEuSJEkNs4RLkiRJDbOES5IkSQ2bUNfCEdEHXALsAiwGZmTm3GH2+SZwTWZeOuKCL3tZTUklSZKkZtV5JvwQYGJmTgFOBS4YZp9zgK1GtdrXv15dMkmSJKlFdZbwqcAsgMycDezevTEipgHLgRtqzCBJkiSNObVdjgJsBizserwsIiZk5tKI2BE4ApgGnDGq1T73OQaOPLLykGrewEB/2xG0FpxX2Zxf2Zxf2ZyfRlJnCX8I6P7t68vMpUN/fgfwfOBGYBKwJCLuz8xZq13trLMYfMNbaoqqpgwM9DM4uKjtGBol51U251c251c251e2Jt5A1VnCbwMOAr4SEZOBOSs3ZOZ7V/45Is4Cfj9iAZckSZJ6SJ0l/Gpgn4i4HRgHTI+ImcDczLy2xuNKkiRJY1ptJTwzlwPHrPL0fcPsd1ZdGSRJkqSxyJv1SJIkSQ2zhEuSJEkNK6eE33tv2wkkSZKkSpRTwp/xjLYTSJIkSZUop4T/8pdtJ5AkSZIqUU4Jf93r2k4gSZIkVaKcEi5JkiT1CEu4JEmS1DBLuCRJktQwS7gkSZLUMEu4JEmS1LBySvinPtV2AkmSJKkS5ZTwAw5oO4EkSZJUiXJKuCRJktQjyinhU6e2nUCSJEmqRDkl/De/aTuBJEmSVIlySrgkSZLUIyzhkiRJUsMs4ZIkSVLDLOGSJElSw8op4Ycf3nYCSZIkqRLllPBzz207gSRJklSJckq4JEmS1CPKKeGnndZ2AkmSJKkS5ZTwL32p7QSSJElSJcop4ZIkSVKPsIRLkiRJDbOES5IkSQ2zhEuSJEkNK6eEb7NN2wkkSZKkSpRTwm+9te0EkiRJUiXKKeGSJElSjyinhN9wQ9sJJEmSpEqUU8KPPbbtBJIkSVIlyinhkiRJUo+YUNfCEdEHXALsAiwGZmTm3K7txwFHAiuAD2bmN+rKIkmSJI0ldZ4JPwSYmJlTgFOBC1ZuiIhnAe8GXgW8HvhURIyrMYskSZI0ZtRZwqcCswAyczaw+8oNmTkP2CUznwC2BhZk5ooas0iSJEljRm2XowCbAQu7Hi+LiAmZuRQgM5dGxPHA2cDHR7PgwEB/9SnVOOdYFudVNudXNudXNuenkdRZwh8Cun/7+lYW8JUy85MR8WnghojYKzNvWu1qN97I4OCiepKqMQMD/c6xIM6rbM6vbM6vbM6vbE28garzcpTbgAMBImIyMGflhuj4+tB14E/Q+eDm8hFX23bb+pJKkiRJDarzTPjVwD4RcTswDpgeETOBuZl5bUT8FLiDzrej3JCZN4+42sMP1xhVkiRJas64FSsK+TzkpEkrBu+cs+b9NKb5n+fK4rzK5vzK5vzK5vzKNjDQX/u39nmzHkmSJKlhlnBJkiSpYZZwSZIkqWGWcEmSJKlhlnBJkiSpYeWU8LPOajuBJEmSVIlySviRR7adQJIkSapEOSVckiRJ6hHllPA3v7ntBJIkSVIlyinhd9/ddgJJkiSpEuWUcEmSJKlHWMIlSZKkhlnCJUmSpIZZwiVJkqSGlVPCX//6thNIkiRJlSinhH/2s20nkCRJkipRTgmXJEmSekQ5JfzCC9tOIEmSJFXCEi5JkiQ1rJwSLkmSJPUIS7gkSZLUMEu4JEmS1DBLuCRJktSwckr4Rhu1nUCSJEmqRDkl/L/+q+0EkiRJUiXKKeGSJElSjyinhP/4x20nkCRJkipRTgl/y1vaTiBJkiRVopwSLkmSJPUIS7gkSZLUMEu4JEmS1DBLuCRJktQwS7gkSZLUsHJK+Je/3HYCSZIkqRLllPDJk9tOIEmSJFWinBIuSZIk9YgJdS0cEX3AJcAuwGJgRmbO7dr+HuCwoYfXZ+bZIy64ww7w/dk1pZUkSZKaU+eZ8EOAiZk5BTgVuGDlhojYFngb8CpgCrBvROw84mqPPFJfUkmSJKlBdZbwqcAsgMycDezete3XwP6ZuSwzlwMbAY/XmEWSJEkaM2q7HAXYDFjY9XhZREzIzKWZ+QQwLyLGAecB92TmL9a04MBAf01R1STnWBbnVTbnVzbnVzbnp5HUWcIfArp/+/oyc+nKBxExEbgcWAS8ezQLDg4uqjSgmjcw0O8cC+K8yub8yub8yub8ytbEG6g6L0e5DTgQICImA3NWbhg6A34N8NPM/LvMXFZjDkmSJGlMqfNM+NXAPhFxOzAOmB4RM4G5wHjgNcAmEXHA0P6nZeYdq13t3aM6WS5JkiSNebWV8KEPXB6zytP3df154lot+N73gv9ZR5IkST3Am/VIkiRJDSunhB+z6kl1SZIkqUzllPBZs9pOIEmSJFWinBIuSZIk9QhLuCRJktQwS7gkSZLUMEu4JEmS1LBySviOO7adQJIkSapEOSX8G99oO4EkSZJUiXJKuCRJktQjyinhX/xi2wkkSZKkSpRTwk8/ve0EkiRJUiXKKeGSJElSj7CES5IkSQ2zhEuSJEkNs4RLkiRJDbOES5IkSQ0rp4Tfc0/bCSRJkqRKlFPCt9yy7QSSJElSJcop4b/5TdsJJEmSpEqUU8KnTm07gSRJklSJckq4JEmS1CMs4ZIkSVLDLOGSJElSwyzhkiRJUsMs4ZIkSVLDyinhF13UdgJJkiSpEuWU8IMPbjuBJEmSVIlySrgkSZLUI8op4Xvt1XYCSZIkqRLllPBf/artBJIkSVIlyinhkiRJUo+whEuSJEkNs4RLkiRJDbOES5IkSQ2bUNfCEdEHXALsAiwGZmTm3FX2GQBuB3bKzMdHXHDatJqSSpIkSc2q80z4IcDEzJwCnApc0L0xIvYDvg08Z1SrnX9+1fkkSZKkVtRZwqcCswAyczaw+yrblwN7A3+qMYMkSZI05tR2OQqwGbCw6/GyiJiQmUsBMvM7ABExutXOPJOBs8+uOqNaMDDQ33YErQXnVTbnVzbnVzbnp5HUWcIfArp/+/pWFvB1cuWVDB5/8nqHUrsGBvoZHFzUdgyNkvMqm/Mrm/Mrm/MrWxNvoOq8HOU24ECAiJgMzKnxWJIkSVIx6jwTfjWwT0TcDowDpkfETGBuZl5b43ElSZKkMa22Ep6Zy4FjVnn6vmH2m1RXBkmSJGks8mY9kiRJUsPKKeHPfnbbCSRJkqRKlFPCf/SjthNIkiRJlSinhEuSJEk9opwS/t3vtp1AkiRJqkQ5JXzGjLYTSJIkSZUop4RLkiRJPcISLkmSJDWszjtmbhDuvvsuzjjjNCZNehHjxo1j8eLF7Lvv/kybdtio1/jsZ/+FZz7zmeyww07ceustTJ9+VI2JJUmS1LaeKeFfuXEud973h0rXfPlLns1bX/fiNe632267c/bZ5wKwZMkSjjjiLey33xvo7+9fq+Ntt12w3XaxTlklSZJUjp4p4WPFo48+Sl9fH+PHjx92+6WXfpL77vsZjz76KJMmvYjTTz/zz9vuvvsurrnma+yzz/7ccsv3/7xt+vQj+Od//iT33HM3//t/f4G+vj523nlXjj327xt5TZIkSapWOSV81qxFnc5ZAAAMGElEQVQRN7/1dS8e1VnrOvz4x3dx/PFH09fXx4QJE3jPe05h0003fcp+jzzyMP39/Vx44SUsX76ct7/9rQwOPvXs/ZQpU7nkko/z2GOPcf/9v+T5z9+G8ePHc/nl/8JnPnMVEydO5J/+6R+5887ZvPzlk5t4iZIkSapQOSX8JS+BwUVtpxhW9+UoI9lkk4nMnz+fM888nU033ZTHHnuMpUuXPmW/8ePH89rXvp6bb76Re++dw0EHHcpvfvNrFiyYz8knnwB0zrj/9re/5eUvr/zlSJIkqWbllPAlS9pOsN5mz76NP/zhQT74wXOZP38+t9xyEytWrBh23ze+8WDOO+/DLFy4gJkz38vChQt59rOfw4UXXsKECRO4/vrr2G677Rt+BZIkSapCOSV8++3hzjltp1gvL33pDnzuc5/l6KOPZOONN+Z5z3s+8+YNDrvv8573fAD23PO19PX1seWWW/I3f/M2jj/+aJYtW8Zzn/s8Xve6fZqML0mSpIqMW92Z2DFn0qQVg4WXcMHAQD+DY/SyIj2V8yqb8yub8yub8yvbwED/uLqPUc6Z8IJcc83X+c53nvpB0mOOOZ4dd9y5hUSSJEkaSyzhNTj44Ddz8MFvbjuGJEmSxihvWy9JkiQ1zBIuSZIkNaycEv7+97edQJIkSapEOSX8qKPaTlC7adMOYvHixW3HkCRJUs3KKeGSJElSjyjn21EOOww+cdmIu2y1247DPv/ou0/g8XcdDUD/u49iox/e8ZR9nthtdxZ9+nMATLzqc2x64fn86cf3rjHW9ddfxw9+cDOPPvoICxYsYPr0GXzykxfyhS98lU022YRPfeoT/MVfTGLrrZ/Lpz71CTbaaCPe9KZD6e/fjCuu6Lye7bYLTjnlNAAuuOAj/O53vwXgwx8+n/Hj+/jIR87h4YcXsXDhAg466FAOPXQaX//6v3HDDd+gr6+PnXfeleOOO5EHH/w9H/3oh1myZDEbb7wJ733v6WyxxZacccapPPLIIyxe/DjHHnsCL3vZ7mt8XZIkSapPOSV89uy2E6zWY489ysc+djELFsznqKPeyfLly4fdb8mSJVx22ZUsXbqUww47lMsuu5Itt9yKK664jD/84Q8AvOENB7PLLrvyoQ+dxZ13/pBttnkBe++9L695zeuYN2+Q448/mkMPncb111/HSSedwo477sTVV3+VpUuXcvHFFzFt2t8wZcoe3HXXj7j00k/y9rdP509/+iMXXngJ8+fP59e/fqDJvzWSJEkaRjklfBRGc+Z60SUjn00HePztR/L4248c9XF33fVl9PX1sdVWz6S/fzMeeOBXf97WfUfSF77wLwBYuHAB/f39bLnlVgBMn/7/r3d/yUteAsBWWz2TxYsf55nPfCZf+coXufnmm9h006ezdOlSAE4//Qy+9KV/5dJLP8EOO+wEwC9/OZerrrqCL3zhSgAmTJjAttv+JW9+81s566z3s3TpUqZNO2zUr0uSJEn16KkS3pbM+wD405/+yCOPPMJznrM1f/zjPJ773Ocxd+4vmDTpRQD09XXugLrlllvx8MMP89BDC9lss8258MLz2HffA4ZWe/JdUr/0pavYccedOfTQadx9913cccetAFx77b9z8smnsckmmzBz5vHMmfNTXvjCSRx++N+y00678MAD93PPPT/mv/97Lo8++gjnnXcR8+bN49hj/yd77LFnM39jJEmSNCxLeAX+9Kc/cuKJx/Lwww/zD//wPubNG+SUU05k662fR39//1P27+vrY+bM93HKKSfR19fH9tsHL33pDsOuvccer+b888/l29++gc0335zx48ezZMkS/vIvX8xRR72DLbbYkoGBAf7qr3bkuONO5IILPsKSJUtYvPhxTjzxZLbZ5gVcccWnmTXrm0yYsBHvetff1f23Q5IkSWswrvtyiTFt0qQVg3fOaTvFU1x//XU88MD9HHvs37cdpQgDA/0MDi5qO4ZGyXmVzfmVzfmVzfmVbWCgf9ya91o/5XxF4Z5eQiFJkqTeUM7lKFddBWPwHeWBBx7UdgRJkiQVppwz4ZIkSVKPKKeEX3xx2wkkSZKkSpRTws87r+0EkiRJUiXKKeGSJElSj7CES5IkSQ2r7dtRIqIPuATYBVgMzMjMuV3bjwL+DlgKnJOZ36griyRJkjSW1Hkm/BBgYmZOAU4FLli5ISK2Bk4A9gD2A86NiE1qzCJJkiSNGXWW8KnALIDMnA3s3rXtFcBtmbk4MxcCc4Gda8wiSZIkjRl13qxnM2Bh1+NlETEhM5cOs20RsPmIq91//7iByiOqDQMD/W1H0FpwXmVzfmVzfmVzfhpJnWfCHwK6f/v6hgr4cNv6gQU1ZpEkSZLGjDpL+G3AgQARMRmY07XtR8CeETExIjYHXgrcW2MWSZIkacwYt2LFiloW7vp2lJ2BccB0OqV8bmZeO/TtKEfTeSPw4cz8Wi1BJEmSpDGmthIuSZIkaXjerEeSJElqmCVckiRJalidX1EIQERsBFwOTAI2Ac4BfgZ8DlhB5wOZx2Xm8qH9Xwz8e2buOPT4WcAXgacBvwOmZ+ajqznWx4DMzEuHHr8HOGxo8/WZeXYNL3GDsL5z7FrnJGDrzDx1mGMMO2vnuPbanNfQtj7gm8A1K/951Oi1/M/bAcCZQ7vdPXQcr1tcCy3P72TgcGA5nc9bXV3Ha+xlTcxvdftExEHAGXTuJn55Zl5W6YvrcS3P7nDgJGAZ8B/Au1ceZ3WaOBP+t8AfM3NP4ADgk8A/Ax8Yem4ccDBARLwd+DLwrK6fPwP44tC+99C51f2TRMRARNwAvKnruW2BtwGvAqYA+0aENwRad+s1x4h4WkT8K3DcCMd4yqyd4zprZV5d284Btqru5Wxw2vrnrR84D3hjZk4G7ufJ/z7W6LQ1vy3o3I16CrAvcGHVL2wDUfv8httnqEB+jM7sXgMcPXSHcY1eW7N7Gp3/39srM19F5943b1xT2CZK+L8B/9j1eCmwG3Dz0OMbgL2H/jyfzi9etz/feXOVfbs9AzgLuKrruV8D+2fmsqF3IhsBj6/bSxDrP8eJwOeBD41wjOFm7RzXTVvzIiKm0TkLd8M6Zld783sVna+TvSAifgA8mJmD6/gaNmRtze8R4AHg6UN/jXgWTqvVxPyG2+eldL5Bbn5mLgFuBfZclxewAWtrdouBV3VdqTGBUXSV2kt4Zj6cmYuGzrB8FfgAMK7rP2/++W6ZmfmNzHxklSW676457J01M/NXmfnDVZ57IjPnRcS4iDgfuCczf1HdK9uwrO8ch/6l8u01HOYps3aO66ateUXEjsARdM7SaR21NT86Z4T2At5H5yzSSRGxfRWvaUPS4vygc+LiZ3QuJfr4er+YDVAT81vNPmt/N3E9SVuzy8zlmfkgQET8PZ2Tw99ZU95GPpgZES8AbgKuyswv8uR352u6W2b33TX7gQURMS0ivj/0124jHHci8IWhn3v3+rwGrfcch1tvatcc38Awsx7azzmug5bm9Q7g+cCNwJHAzIjYf71eyAaqpfn9EbgzM3+fmQ8DtwC7rudL2SC1NL8DgOcCLwJeCBwSEa9Yv1eyYWpgfsPxbuIVaGl2RETf0MnCfYC3jOazNE18MPM5wLeB4zPze0NP3xMRr83M79P5l8ZNIyyx8s6bnxva9weZ+VU673BGOu444Brgxsz8X+v1IlTFHJ8iM28FXtt1jP1ZZdbOcd20Na/uGUXEWcDvM3MWWittzQ/4MbDj0If+FgCTAT8YtpZanN984DFgcWauiIgFwBbr9WI2QE3MbzV+DmwXEVsBDwOvBs5fm+Ns6FqcHcC/0Lks5ZA1fSBzpdpLOHA6sCXwjxGx8jqdE4GPR8TGdH7pRirU5wBXRucOm/Po/Kfu0TiEzrU+m0Tn0/4Ap2XmHWv7AgSs/xxHY7hZO8d109a8VI1W5peZj0TEacC3hvb5Smbeu57H2RC1Ob+9gdkRsZzONcVr/E/ieoom5vcUmflERMyk889fH51vR/lt1cfpca3MLiJeBryLzpvhGyMC4KJcw7cTecdMSZIkqWHerEeSJElqmCVckiRJapglXJIkSWqYJVySJElqmCVckiRJapglXJIkSWqYJVySJElqmCVckiRJatj/Aygi7J6T0tbMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "id = 14729\n",
    "days_since_birth = 365\n",
    "sp_trans = df.loc[df['CustomerID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'InvoiceDate');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, this customer had only purchased once and has dropped off for a long time with a 100% chance that he is dead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating customer lifetime value using gamma-gamma model of monetary value\n",
    "We are now taking into account the economic value of each transaction. To estimate this we use the Gamma-Gamma submodel presented by Dr. Peter Fader and Dr. Bruce Hardie from Wharton, to predict likely spend per transaction in the future at the customer level.\n",
    "\n",
    "We are only estimating the customers who had at least one repeat purchase with us. Therefore, we are estimating for 2,790 customers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            frequency  recency      T  monetary_value  predicted_purchases\n",
      "CustomerID                                                                \n",
      "12347.0           6.0    365.0  367.0      599.701667             0.015657\n",
      "12348.0           3.0    283.0  358.0      301.480000             0.008957\n",
      "12352.0           6.0    260.0  296.0      368.256667             0.018699\n",
      "12356.0           2.0    303.0  325.0      269.905000             0.007172\n",
      "12358.0           1.0    149.0  150.0      683.200000             0.008339\n",
      "2790\n"
     ]
    }
   ],
   "source": [
    "returning_customers_summary = data[data['frequency']>0]\n",
    "print(returning_customers_summary.head())\n",
    "print(len(returning_customers_summary))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "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>monetary_value</th>\n",
       "      <th>frequency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>monetary_value</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.015882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>frequency</th>\n",
       "      <td>0.015882</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                monetary_value  frequency\n",
       "monetary_value        1.000000   0.015882\n",
       "frequency             0.015882   1.000000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returning_customers_summary[['monetary_value', 'frequency']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.GammaGammaFitter: fitted with 2790 subjects, p: 2.10, q: 3.45, v: 485.57>\n"
     ]
    }
   ],
   "source": [
    "from lifetimes import GammaGammaFitter\n",
    "ggf = GammaGammaFitter(penalizer_coef = 0)\n",
    "ggf.fit(returning_customers_summary['frequency'],\n",
    "        returning_customers_summary['monetary_value'])\n",
    "print(ggf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After applying Gamma-Gamma model, now we can estimate average transaction value for each customer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CustomerID\n",
      "12346.0    416.917653\n",
      "12347.0    569.988800\n",
      "12348.0    333.762672\n",
      "12349.0    416.917653\n",
      "12350.0    416.917653\n",
      "12352.0    376.166863\n",
      "12353.0    416.917653\n",
      "12354.0    416.917653\n",
      "12355.0    416.917653\n",
      "12356.0    324.008941\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(ggf.conditional_expected_average_profit(\n",
    "        data['frequency'],\n",
    "        data['monetary_value']\n",
    "    ).head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CustomerID\n",
      "12346.0     295.302031\n",
      "12347.0    3012.000659\n",
      "12348.0    1008.993210\n",
      "12349.0    1337.116374\n",
      "12350.0     306.987570\n",
      "12352.0    2373.903706\n",
      "12353.0     426.161319\n",
      "12354.0     386.524682\n",
      "12355.0     411.105078\n",
      "12356.0     784.279880\n",
      "Name: clv, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "bgf.fit(data['frequency'], data['recency'], data['T'])\n",
    "\n",
    "print(ggf.customer_lifetime_value(\n",
    "    bgf, #the model to use to predict the number of future transactions\n",
    "    data['frequency'],\n",
    "    data['recency'],\n",
    "    data['T'],\n",
    "    data['monetary_value'],\n",
    "    time=12, # months\n",
    "    discount_rate=0.01 # monthly discount rate ~ 12.7% annually\n",
    ").head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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