Monte_Carlo_Simulationv2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monte Carlo Simulation with Python\n",
    "\n",
    "Notebook to accompany article on [Practical Business Python](https://pbpython.com/monte-carlo.html)\n",
    "\n",
    "Update to use numpy for faster loops based on comments [here](https://www.reddit.com/r/Python/comments/arxwkm/monte_carlo_simulation_with_python/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the variables for the Percent to target based on historical results\n",
    "avg = 1\n",
    "std_dev = .1\n",
    "num_reps = 500\n",
    "num_simulations = 100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show an example of calculating the percent to target\n",
    "pct_to_target = np.random.normal(\n",
    "    avg,\n",
    "    std_dev,\n",
    "    size=(num_reps, num_simulations)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.79328531, 0.99211018, 1.14343423, ..., 0.83737887, 0.93507967,\n",
       "        0.86079851],\n",
       "       [1.03126742, 1.04414961, 1.08119495, ..., 0.98607625, 1.01161899,\n",
       "        0.96872644],\n",
       "       [1.08616345, 0.93970666, 1.07594111, ..., 0.94057821, 1.00399945,\n",
       "        1.05325946],\n",
       "       ...,\n",
       "       [1.10388204, 0.90397305, 0.96005999, ..., 0.88810244, 1.18064642,\n",
       "        0.94066897],\n",
       "       [1.07581302, 0.92552317, 1.08256074, ..., 0.91934988, 1.06668758,\n",
       "        1.05969099],\n",
       "       [1.12755095, 0.95080038, 0.978849  , ..., 1.0094155 , 0.94359533,\n",
       "        1.06332923]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pct_to_target[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Another example for the sales target distribution\n",
    "sales_target_values = [75_000, 100_000, 200_000, 300_000, 400_000, 500_000]\n",
    "sales_target_prob = [.3, .3, .2, .1, .05, .05]\n",
    "sales_target = np.random.choice(sales_target_values, p=sales_target_prob, \n",
    "                                size=(num_reps, num_simulations))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 75000, 200000,  75000, ...,  75000, 100000, 200000],\n",
       "       [200000,  75000, 100000, ..., 200000, 100000, 100000],\n",
       "       [400000,  75000, 100000, ..., 500000, 200000,  75000],\n",
       "       ...,\n",
       "       [500000,  75000, 500000, ...,  75000,  75000,  75000],\n",
       "       [ 75000, 100000,  75000, ...,  75000, 500000, 100000],\n",
       "       [100000,  75000,  75000, ..., 100000, 100000,  75000]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales_target[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "commission_percentages = np.take(\n",
    "    np.array([0.04, 0.03, 0.02]),\n",
    "    np.digitize(pct_to_target, bins=[.9, .99, 10])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    26992625\n",
       "1    15075317\n",
       "0     7932058\n",
       "dtype: int64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(np.digitize(pct_to_target, bins=[.9, .99, 10]).flatten()).value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02    26992625\n",
       "0.03    15075317\n",
       "0.04     7932058\n",
       "dtype: int64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# frequencies\n",
    "pd.DataFrame(commission_percentages.flatten()).value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.04, 0.02, 0.02, ..., 0.04, 0.03, 0.04],\n",
       "       [0.02, 0.02, 0.02, ..., 0.03, 0.02, 0.03],\n",
       "       [0.02, 0.03, 0.02, ..., 0.03, 0.02, 0.02],\n",
       "       ...,\n",
       "       [0.02, 0.03, 0.03, ..., 0.04, 0.02, 0.03],\n",
       "       [0.02, 0.03, 0.02, ..., 0.03, 0.02, 0.02],\n",
       "       [0.02, 0.03, 0.03, ..., 0.02, 0.03, 0.02]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "commission_percentages[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_commissions = (commission_percentages * sales_target).sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "96546.42131435724"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_commissions.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "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>Total_Commissions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2838250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2786750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2795500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3054750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2831750.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Total_Commissions\n",
       "0          2838250.0\n",
       "1          2786750.0\n",
       "2          2795500.0\n",
       "3          3054750.0\n",
       "4          2831750.0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show how to create the dataframe\n",
    "df = pd.DataFrame(data={'Total_Commissions': total_commissions})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Commissions Distribution'}, ylabel='Frequency'>"
      ]
     },
     "execution_count": 53,
     "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": [
    "df.plot(kind='hist', title='Commissions Distribution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Total_Commissions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.000000e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.831683e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.654690e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.472750e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.765750e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.830250e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.896500e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.278500e+06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "       Total_Commissions\n",
       "count       1.000000e+05\n",
       "mean        2.831683e+06\n",
       "std         9.654690e+04\n",
       "min         2.472750e+06\n",
       "25%         2.765750e+06\n",
       "50%         2.830250e+06\n",
       "75%         2.896500e+06\n",
       "max         3.278500e+06"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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