Calculating-CLV-Using-BG NBD-model .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c34b77ae",
   "metadata": {},
   "source": [
    "### Estimating Customer Life Time Value. \n",
    "In a contractual churn setting, like a mobile phone network or a broadband provider, its realatively straightforward to compute Life Time Value or if the customer are 'Alive' as its known in the world of CLV. In non-contractual churn settings, like most ecommerce businesses, the time of a customer’s “death” isn’t directly observed, so you never really know which ones are alive or dead.\n",
    "\n",
    "Customers often vary dramatically in their behaviour - some order weekly and others order annually. There’s no such thing as “typical customer.” If a customer normally orders from you every week and hasn’t shopped for a year, do you really think they’re still alive?\n",
    "\n",
    "#### Calculating CLV\n",
    "\n",
    "Here we’re going to use - the Beta Geometric Negative Binomial Distribution or BG/NBD model - to predict the following:\n",
    "\n",
    "    - Which customers are still customers\n",
    "    - Who will order again in the next period\n",
    "    - The number of orders each customer will place\n",
    "    - The average order value of each customer’s order\n",
    "    - The total amount each customer will generate for the business\n",
    "    \n",
    "#### Intution Behind BG/NBD Model\n",
    "\n",
    "https://lifetimes.readthedocs.io/en/latest/Quickstart.html#estimating-customer-lifetime-value-using-the-gamma-gamma-model\n",
    "\n",
    "Pete Fader's publications\n",
    "https://scholar.google.com/citations?user=NYOYpwQAAAAJ\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ee6828dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install lifetimes\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5720f4e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "pd.set_option('display.float_format', lambda x: '%.3f' % x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "74c072ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('Segmentation.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "df76e9af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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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>CustomerID</th>\n",
       "      <th>Recency</th>\n",
       "      <th>Tenure</th>\n",
       "      <th>Frequency</th>\n",
       "      <th>MonetaryValue</th>\n",
       "      <th>Segment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346</td>\n",
       "      <td>326</td>\n",
       "      <td>326</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000</td>\n",
       "      <td>Fence Sitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12349</td>\n",
       "      <td>19</td>\n",
       "      <td>19</td>\n",
       "      <td>73</td>\n",
       "      <td>1757.550</td>\n",
       "      <td>Potential</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12350</td>\n",
       "      <td>310</td>\n",
       "      <td>310</td>\n",
       "      <td>17</td>\n",
       "      <td>334.400</td>\n",
       "      <td>Fence Sitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12353</td>\n",
       "      <td>204</td>\n",
       "      <td>204</td>\n",
       "      <td>4</td>\n",
       "      <td>89.000</td>\n",
       "      <td>Fence Sitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12354</td>\n",
       "      <td>232</td>\n",
       "      <td>232</td>\n",
       "      <td>58</td>\n",
       "      <td>1079.400</td>\n",
       "      <td>Fence Sitter</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID  Recency  Tenure  Frequency  MonetaryValue       Segment\n",
       "0       12346      326     326          2          0.000  Fence Sitter\n",
       "1       12349       19      19         73       1757.550     Potential\n",
       "2       12350      310     310         17        334.400  Fence Sitter\n",
       "3       12353      204     204          4         89.000  Fence Sitter\n",
       "4       12354      232     232         58       1079.400  Fence Sitter"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Import Dataset that is already transformed into RFM as the model expects. \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "09d2f735",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3046, 6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e6dc74f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#'Segement' is not needed by model so we drop it\n",
    "data = df.drop(['Segment'],axis=1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "07f66680",
   "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>CustomerID</th>\n",
       "      <th>Recency</th>\n",
       "      <th>Tenure</th>\n",
       "      <th>Frequency</th>\n",
       "      <th>MonetaryValue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346</td>\n",
       "      <td>326</td>\n",
       "      <td>326</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12349</td>\n",
       "      <td>19</td>\n",
       "      <td>19</td>\n",
       "      <td>73</td>\n",
       "      <td>1757.550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12350</td>\n",
       "      <td>310</td>\n",
       "      <td>310</td>\n",
       "      <td>17</td>\n",
       "      <td>334.400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12353</td>\n",
       "      <td>204</td>\n",
       "      <td>204</td>\n",
       "      <td>4</td>\n",
       "      <td>89.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12354</td>\n",
       "      <td>232</td>\n",
       "      <td>232</td>\n",
       "      <td>58</td>\n",
       "      <td>1079.400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID  Recency  Tenure  Frequency  MonetaryValue\n",
       "0       12346      326     326          2          0.000\n",
       "1       12349       19      19         73       1757.550\n",
       "2       12350      310     310         17        334.400\n",
       "3       12353      204     204          4         89.000\n",
       "4       12354      232     232         58       1079.400"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d535b2bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 5)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We look at MonetaryValue that is less then or equal to Zero\n",
    "data[data['MonetaryValue']<=0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "104607ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Create a mask for negative values\n",
    "negative_mask = data['MonetaryValue']<=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "144c5c91",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Drop the negative values\n",
    "data_cleaned = data.loc[~negative_mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f9ead11e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>CustomerID</th>\n",
       "      <th>Recency</th>\n",
       "      <th>Tenure</th>\n",
       "      <th>Frequency</th>\n",
       "      <th>MonetaryValue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12349</td>\n",
       "      <td>19</td>\n",
       "      <td>19</td>\n",
       "      <td>73</td>\n",
       "      <td>1757.550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12350</td>\n",
       "      <td>310</td>\n",
       "      <td>310</td>\n",
       "      <td>17</td>\n",
       "      <td>334.400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12353</td>\n",
       "      <td>204</td>\n",
       "      <td>204</td>\n",
       "      <td>4</td>\n",
       "      <td>89.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12354</td>\n",
       "      <td>232</td>\n",
       "      <td>232</td>\n",
       "      <td>58</td>\n",
       "      <td>1079.400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12355</td>\n",
       "      <td>214</td>\n",
       "      <td>214</td>\n",
       "      <td>13</td>\n",
       "      <td>459.400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>12357</td>\n",
       "      <td>33</td>\n",
       "      <td>33</td>\n",
       "      <td>131</td>\n",
       "      <td>6207.670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12358</td>\n",
       "      <td>2</td>\n",
       "      <td>151</td>\n",
       "      <td>19</td>\n",
       "      <td>1168.060</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID  Recency  Tenure  Frequency  MonetaryValue\n",
       "1       12349       19      19         73       1757.550\n",
       "2       12350      310     310         17        334.400\n",
       "3       12353      204     204          4         89.000\n",
       "4       12354      232     232         58       1079.400\n",
       "5       12355      214     214         13        459.400\n",
       "6       12357       33      33        131       6207.670\n",
       "7       12358        2     151         19       1168.060"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cleaned Dataset\n",
    "data_cleaned.head(7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fedda1d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2998, 5)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_cleaned.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b78f26b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0726f966",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "59.238825883922615"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_cleaned.Frequency.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bdec8bc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CustomerID      15634.980\n",
       "Recency           114.352\n",
       "Tenure            186.520\n",
       "Frequency          59.239\n",
       "MonetaryValue    1095.920\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_cleaned.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "38a4fc69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'corr':                CustomerID  Recency  Tenure  Frequency  MonetaryValue\n",
       " CustomerID          1.000   -0.119   0.205      0.128          0.076\n",
       " Recency            -0.119    1.000   0.587     -0.164         -0.091\n",
       " Tenure              0.205    0.587   1.000      0.130          0.103\n",
       " Frequency           0.128   -0.164   0.130      1.000          0.243\n",
       " MonetaryValue       0.076   -0.091   0.103      0.243          1.000,\n",
       " 'ax': <Axes: >}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check the Correlation between RFM values \n",
    "from dython.nominal import associations\n",
    "associations(data_cleaned)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fda1769",
   "metadata": {},
   "source": [
    "#### Relax the assumption that Monetary Value & Purchase Frequency are not Correlated"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc1524fe",
   "metadata": {},
   "source": [
    "The Gamma-Gamma submodel, assumes that there is no relationship between the monetary value and the purchase frequency. In practice we need to check whether the Pearson correlation between the two vectors is close to 0 in order to use this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ea180a5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SignificanceResult(statistic=-0.38195099313703895, pvalue=9.796771596195511e-105)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Our Dataset meets the criteria, p-value is extremely small\n",
    "import scipy\n",
    "\n",
    "scipy.stats.spearmanr(data_cleaned.Recency, data_cleaned.MonetaryValue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "dcc65a9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SignificanceResult(statistic=-0.4220920147437886, pvalue=7.719285272847262e-130)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.spearmanr(data_cleaned.Recency, data_cleaned.MonetaryValue * data_cleaned.Frequency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9dbe3b13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lifetimes.BetaGeoFitter: fitted with 2998 subjects, a: 10.04, alpha: 0.03, b: 1128.18, r: 0.25>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Import GammaGammaFitter, BetaGeoFitter\n",
    "from lifetimes import GammaGammaFitter, BetaGeoFitter\n",
    "bgf = BetaGeoFitter(penalizer_coef=0.0)\n",
    "bgf.fit(data_cleaned['Frequency'], data_cleaned['Recency'], data_cleaned['Tenure'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "74c8b354",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nitinjoseph/opt/anaconda3/lib/python3.9/site-packages/lifetimes/fitters/beta_geo_fitter.py:256: RuntimeWarning: overflow encountered in scalar power\n",
      "  denominator = 1 + (x > 0) * (a / (b + x - 1)) * ((alpha + T) / (alpha + recency)) ** (r + x)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Expected Number of Future Purchases for 1 Unit of Time,\\nby Frequency and Recency of a Customer'}, xlabel=\"Customer's Historical Frequency\", ylabel=\"Customer's Recency\">"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_frequency_recency_matrix\n",
    "\n",
    "plot_frequency_recency_matrix(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "03e15d7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Probability Customer is Alive,\\nby Frequency and Recency of a Customer'}, xlabel=\"Customer's Historical Frequency\", ylabel=\"Customer's Recency\">"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_probability_alive_matrix\n",
    "\n",
    "plot_probability_alive_matrix(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f251e712",
   "metadata": {},
   "source": [
    "Probability that customer is still 'alive'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "43f19b84",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Model expects Frequency greater than Zero\n",
    "data_repeat = data_cleaned[data_cleaned.Frequency>0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "38f65489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lifetimes.GammaGammaFitter: fitted with 2998 subjects, p: 0.06, q: 2.15, v: 23340.09>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggf = GammaGammaFitter(penalizer_coef=0.0)\n",
    "ggf.fit(data_repeat.Frequency, data_repeat.MonetaryValue)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86b1ad91",
   "metadata": {},
   "source": [
    "#### Fit the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5e89147d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1    1639.844\n",
      "2     795.791\n",
      "3    1009.505\n",
      "4    1109.358\n",
      "5     902.667\n",
      "6    5559.435\n",
      "7    1183.512\n",
      "8     856.347\n",
      "9    1291.756\n",
      "10    723.188\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(ggf.conditional_expected_average_profit(\n",
    "        data_cleaned['Frequency'],\n",
    "        data_cleaned['MonetaryValue']\n",
    "    ).head(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe7dc1bc",
   "metadata": {},
   "source": [
    "#### Expected Average Profit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "33ee9da4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected conditional average profit: 1368.4752215617332, Average profit: 1074.315536112935\n"
     ]
    }
   ],
   "source": [
    "print('Expected conditional average profit: %s, Average profit: %s' % (\n",
    "    ggf.conditional_expected_average_profit(\n",
    "        data_cleaned['Frequency'],\n",
    "        data_cleaned['MonetaryValue']\n",
    "    ).mean(),\n",
    "    data[data['Frequency']>0]['MonetaryValue'].mean()\n",
    "))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ede0ef9d",
   "metadata": {},
   "source": [
    "#### CLV for each customer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2ca8e8b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1    213482.859\n",
      "2     13568.091\n",
      "3      6759.006\n",
      "4     66051.599\n",
      "5     16927.331\n",
      "6    758653.350\n",
      "7         0.000\n",
      "8      9640.990\n",
      "9         0.000\n",
      "10    17099.801\n",
      "Name: clv, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#Output just the first 10\n",
    "print(ggf.customer_lifetime_value(\n",
    "    bgf, #the model to use to predict the number of future transactions\n",
    "    data_cleaned['Frequency'],\n",
    "    data_cleaned['Recency'],\n",
    "    data_cleaned['Tenure'],\n",
    "    data_cleaned['MonetaryValue'],\n",
    "    time=12, # months\n",
    "    discount_rate=0.01 # monthly discount rate ~ 12.7% annually\n",
    ").head(10))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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