diff --git a/README.md b/README.md
index e4a98e6..a5dd78e 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,5 @@
 - 👋 Hi, I’m @bala35210
-- 👀 I’m interested in data analyst, scientist and ML/AI engineer.
+- 👀 I’m interested in data analyst, scientist and ML/AI.
 - 🌱 I’m currently learning Machine Learning and Data Analytics.
 - 💞️ I’m looking to collaborate on data analyst projects.
 - 📫 You can reach me @ Linkedin: https://www.linkedin.com/in/balakumaran-selvaraji-9b4a1b105/
diff --git a/Statistics/Calculations.pdf b/Statistics/Calculations.pdf
new file mode 100644
index 0000000..8962f6a
Binary files /dev/null and b/Statistics/Calculations.pdf differ
diff --git a/Statistics/ML and MM Fit using scipy.ipynb b/Statistics/ML and MM Fit using scipy.ipynb
new file mode 100644
index 0000000..0234a89
--- /dev/null
+++ b/Statistics/ML and MM Fit using scipy.ipynb	
@@ -0,0 +1,1166 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import scipy.stats as st\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "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>Sno</th>\n",
+       "      <th>Order ID</th>\n",
+       "      <th>Date of placing order</th>\n",
+       "      <th>Order Dispatch date</th>\n",
+       "      <th>Logistics Type</th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Segment</th>\n",
+       "      <th>Country</th>\n",
+       "      <th>City</th>\n",
+       "      <th>State</th>\n",
+       "      <th>...</th>\n",
+       "      <th>Discount</th>\n",
+       "      <th>Profit</th>\n",
+       "      <th>Unnamed: 20</th>\n",
+       "      <th>log10000</th>\n",
+       "      <th>Total Sales</th>\n",
+       "      <th>Month</th>\n",
+       "      <th>Quarter</th>\n",
+       "      <th>Unnamed: 25</th>\n",
+       "      <th>Unnamed: 26</th>\n",
+       "      <th>Unnamed: 27</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>740</td>\n",
+       "      <td>CA-2014-112326</td>\n",
+       "      <td>2014-01-04</td>\n",
+       "      <td>2014-01-08</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Phillina Ober</td>\n",
+       "      <td>Home Office</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Naperville</td>\n",
+       "      <td>Illinois</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>4.2717</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.267823</td>\n",
+       "      <td>38127.933</td>\n",
+       "      <td>Jan</td>\n",
+       "      <td>Q1</td>\n",
+       "      <td>39360.06045</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>741</td>\n",
+       "      <td>CA-2014-112326</td>\n",
+       "      <td>2014-01-04</td>\n",
+       "      <td>2014-01-08</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Phillina Ober</td>\n",
+       "      <td>Home Office</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Naperville</td>\n",
+       "      <td>Illinois</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>-64.7748</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.608936</td>\n",
+       "      <td>21452.645</td>\n",
+       "      <td>Feb</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>742</td>\n",
+       "      <td>CA-2014-112326</td>\n",
+       "      <td>2014-01-04</td>\n",
+       "      <td>2014-01-08</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Phillina Ober</td>\n",
+       "      <td>Home Office</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Naperville</td>\n",
+       "      <td>Illinois</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.8</td>\n",
+       "      <td>-5.4870</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.137251</td>\n",
+       "      <td>97859.6638</td>\n",
+       "      <td>Mar</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1760</td>\n",
+       "      <td>CA-2014-141817</td>\n",
+       "      <td>2014-01-05</td>\n",
+       "      <td>2014-01-12</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Mick Brown</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Philadelphia</td>\n",
+       "      <td>Pennsylvania</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>4.8840</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.322709</td>\n",
+       "      <td>81724.5361</td>\n",
+       "      <td>Apr</td>\n",
+       "      <td>Q2</td>\n",
+       "      <td>55751.25475</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>593</td>\n",
+       "      <td>CA-2014-135405</td>\n",
+       "      <td>2014-01-09</td>\n",
+       "      <td>2014-01-13</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Melanie Seite</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Laredo</td>\n",
+       "      <td>Texas</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>1.1680</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.242633</td>\n",
+       "      <td>70289.3068</td>\n",
+       "      <td>May</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4995</th>\n",
+       "      <td>907</td>\n",
+       "      <td>CA-2017-143259</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Patrick O'Donnell</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>New York City</td>\n",
+       "      <td>New York</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>12.1176</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.627346</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4996</th>\n",
+       "      <td>908</td>\n",
+       "      <td>CA-2017-143259</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Patrick O'Donnell</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>New York City</td>\n",
+       "      <td>New York</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>2.7279</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.489677</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4997</th>\n",
+       "      <td>909</td>\n",
+       "      <td>CA-2017-143259</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Patrick O'Donnell</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>New York City</td>\n",
+       "      <td>New York</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>19.7910</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.430609</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4998</th>\n",
+       "      <td>1297</td>\n",
+       "      <td>CA-2017-115427</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Erica Bern</td>\n",
+       "      <td>Corporate</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Fairfield</td>\n",
+       "      <td>California</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>4.5188</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.285785</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4999</th>\n",
+       "      <td>1298</td>\n",
+       "      <td>CA-2017-115427</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Erica Bern</td>\n",
+       "      <td>Corporate</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Fairfield</td>\n",
+       "      <td>California</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>6.4750</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.329097</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5000 rows × 28 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "       Sno        Order ID Date of placing order Order Dispatch date  \\\n",
+       "0      740  CA-2014-112326            2014-01-04          2014-01-08   \n",
+       "1      741  CA-2014-112326            2014-01-04          2014-01-08   \n",
+       "2      742  CA-2014-112326            2014-01-04          2014-01-08   \n",
+       "3     1760  CA-2014-141817            2014-01-05          2014-01-12   \n",
+       "4      593  CA-2014-135405            2014-01-09          2014-01-13   \n",
+       "...    ...             ...                   ...                 ...   \n",
+       "4995   907  CA-2017-143259            2017-12-30          2018-01-03   \n",
+       "4996   908  CA-2017-143259            2017-12-30          2018-01-03   \n",
+       "4997   909  CA-2017-143259            2017-12-30          2018-01-03   \n",
+       "4998  1297  CA-2017-115427            2017-12-30          2018-01-03   \n",
+       "4999  1298  CA-2017-115427            2017-12-30          2018-01-03   \n",
+       "\n",
+       "      Logistics Type               Name      Segment        Country  \\\n",
+       "0     Standard Class      Phillina Ober  Home Office  United States   \n",
+       "1     Standard Class      Phillina Ober  Home Office  United States   \n",
+       "2     Standard Class      Phillina Ober  Home Office  United States   \n",
+       "3     Standard Class         Mick Brown     Consumer  United States   \n",
+       "4     Standard Class      Melanie Seite     Consumer  United States   \n",
+       "...              ...                ...          ...            ...   \n",
+       "4995  Standard Class  Patrick O'Donnell     Consumer  United States   \n",
+       "4996  Standard Class  Patrick O'Donnell     Consumer  United States   \n",
+       "4997  Standard Class  Patrick O'Donnell     Consumer  United States   \n",
+       "4998  Standard Class         Erica Bern    Corporate  United States   \n",
+       "4999  Standard Class         Erica Bern    Corporate  United States   \n",
+       "\n",
+       "               City         State  ...  Discount   Profit Unnamed: 20  \\\n",
+       "0        Naperville      Illinois  ...       0.2   4.2717           1   \n",
+       "1        Naperville      Illinois  ...       0.2 -64.7748           1   \n",
+       "2        Naperville      Illinois  ...       0.8  -5.4870           1   \n",
+       "3      Philadelphia  Pennsylvania  ...       0.2   4.8840           1   \n",
+       "4            Laredo         Texas  ...       0.2   1.1680           1   \n",
+       "...             ...           ...  ...       ...      ...         ...   \n",
+       "4995  New York City      New York  ...       0.2  12.1176          12   \n",
+       "4996  New York City      New York  ...       0.0   2.7279          12   \n",
+       "4997  New York City      New York  ...       0.2  19.7910          12   \n",
+       "4998      Fairfield    California  ...       0.2   4.5188          12   \n",
+       "4999      Fairfield    California  ...       0.2   6.4750          12   \n",
+       "\n",
+       "      log10000 Total Sales Month  Quarter  Unnamed: 25  Unnamed: 26  \\\n",
+       "0     0.267823   38127.933   Jan       Q1  39360.06045          NaN   \n",
+       "1     0.608936   21452.645   Feb      NaN          NaN          NaN   \n",
+       "2     0.137251  97859.6638   Mar      NaN          NaN          NaN   \n",
+       "3     0.322709  81724.5361   Apr       Q2  55751.25475          NaN   \n",
+       "4     0.242633  70289.3068   May      NaN          NaN          NaN   \n",
+       "...        ...         ...   ...      ...          ...          ...   \n",
+       "4995  0.627346         NaN   NaN      NaN          NaN          NaN   \n",
+       "4996  0.489677         NaN   NaN      NaN          NaN          NaN   \n",
+       "4997  0.430609         NaN   NaN      NaN          NaN          NaN   \n",
+       "4998  0.285785         NaN   NaN      NaN          NaN          NaN   \n",
+       "4999  0.329097         NaN   NaN      NaN          NaN          NaN   \n",
+       "\n",
+       "      Unnamed: 27  \n",
+       "0             NaN  \n",
+       "1             NaN  \n",
+       "2             NaN  \n",
+       "3             NaN  \n",
+       "4             NaN  \n",
+       "...           ...  \n",
+       "4995          NaN  \n",
+       "4996          NaN  \n",
+       "4997          NaN  \n",
+       "4998          NaN  \n",
+       "4999          NaN  \n",
+       "\n",
+       "[5000 rows x 28 columns]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_excel(r'C:\\Users\\Balakumaran S\\Desktop\\Superstore - Excel.xlsx')\n",
+    "df"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([  1.,   0.,   0.,   3.,  11.,   7.,  20.,  24.,  54.,  57.,  70.,\n",
+       "        111., 131., 158., 188., 220., 257., 240., 237., 226., 251., 237.,\n",
+       "        230., 199., 213., 186., 151., 182., 164., 203., 163., 141., 136.,\n",
+       "        139.,  94.,  92.,  73.,  43.,  35.,  14.,  18.,   4.,   8.,   0.,\n",
+       "          1.,   5.,   2.,   0.,   0.,   1.]),\n",
+       " array([-0.08815426, -0.06461694, -0.04107961, -0.01754229,  0.00599503,\n",
+       "         0.02953235,  0.05306967,  0.07660699,  0.10014431,  0.12368164,\n",
+       "         0.14721896,  0.17075628,  0.1942936 ,  0.21783092,  0.24136824,\n",
+       "         0.26490556,  0.28844289,  0.31198021,  0.33551753,  0.35905485,\n",
+       "         0.38259217,  0.40612949,  0.42966681,  0.45320414,  0.47674146,\n",
+       "         0.50027878,  0.5238161 ,  0.54735342,  0.57089074,  0.59442807,\n",
+       "         0.61796539,  0.64150271,  0.66504003,  0.68857735,  0.71211467,\n",
+       "         0.73565199,  0.75918932,  0.78272664,  0.80626396,  0.82980128,\n",
+       "         0.8533386 ,  0.87687592,  0.90041324,  0.92395057,  0.94748789,\n",
+       "         0.97102521,  0.99456253,  1.01809985,  1.04163717,  1.06517449,\n",
+       "         1.08871182]),\n",
+       " <BarContainer object of 50 artists>)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAPEUlEQVR4nO3df6zdd13H8efLAYvKIsPeLaVrvZMUdUtk4HUQp2a46Mb4oywBUzRjkpli3Awk/MHGH0JimtREQI0CKbAwE9xsZLgaJzomOgmM0S5jW1cnldWttFnHjwjBZKbd2z/Ot/HY3dv7vfecc+85nz4fyc0953O+5573Z7d73ff9fL/nc1NVSJLa8kPrXYAkafwMd0lqkOEuSQ0y3CWpQYa7JDXoRetdAMCGDRtqfn5+vcuQpJmyf//+b1XV3GKPTUW4z8/Ps2/fvvUuQ5JmSpL/XOoxl2UkqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBU/EOVc2++Vv+btHxw7vetMaVSAI7d0lq0rLhnmRzki8kOZjkQJJ3deMfSPLNJA93H9cOPefWJIeSPJHk6klOQJL0Qn2WZU4A76mqh5KcB+xPcm/32Ier6o+GD05yCbAduBR4BfD5JK+qqpPjLFyStLRlO/eqOlZVD3W3vw8cBDad4SnbgDur6rmqehI4BFw+jmIlSf2s6IRqknngNcBXgCuAm5O8HdjHoLv/LoPgf2DoaUdY5IdBkh3ADoAtW7aspnadRTxhK61M7xOqSV4KfAZ4d1V9D/go8ErgMuAY8MFThy7y9HrBQNXuqlqoqoW5uUX3mpckrVKvcE/yYgbB/umqugugqp6pqpNV9Tzwcf5v6eUIsHno6RcBR8dXsiRpOX2ulgnwSeBgVX1oaHzj0GHXAY91t/cC25Ocm+RiYCvw4PhKliQtp8+a+xXA9cCjSR7uxt4HvC3JZQyWXA4D7wSoqgNJ9gCPM7jS5iavlJGktbVsuFfVF1l8Hf2eMzxnJ7BzhLokSSPwHaqS1CDDXZIa5MZhmiivT5fWh527JDXIcJekBrkso3UxruUal32kxdm5S1KDDHdJapDhLkkNMtwlqUGeUFWTljrRCp5s1dnBzl2SGmS4S1KDDHdJapBr7poqZ1orl9SfnbskNchwl6QGGe6S1CDDXZIa5AlVrYgnPKXZYOcuSQ0y3CWpQYa7JDXIcJekBnlCVer4J/vUEjt3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1KBlwz3J5iRfSHIwyYEk7+rGX57k3iRf7z6fP/ScW5McSvJEkqsnOQFJ0gv1uc79BPCeqnooyXnA/iT3Ar8F3FdVu5LcAtwCvDfJJcB24FLgFcDnk7yqqk5OZgrSbPP6ek3Csp17VR2rqoe6298HDgKbgG3A7d1htwNv7m5vA+6squeq6kngEHD5mOuWJJ3Bitbck8wDrwG+AlxYVcdg8AMAuKA7bBPw9NDTjnRjkqQ10nv7gSQvBT4DvLuqvpdkyUMXGatFvt4OYAfAli1b+pYhjcw96XU26NW5J3kxg2D/dFXd1Q0/k2Rj9/hG4Hg3fgTYPPT0i4Cjp3/NqtpdVQtVtTA3N7fa+iVJi+hztUyATwIHq+pDQw/tBW7obt8A3D00vj3JuUkuBrYCD46vZEnScvosy1wBXA88muThbux9wC5gT5IbgaeAtwJU1YEke4DHGVxpc5NXykjS2lo23Kvqiyy+jg5w1RLP2QnsHKEuSdIIfIeqJDXIcJekBhnuktQgw12SGuTfUNWifKOPNNvs3CWpQXbu0jLctVGzyM5dkhpkuEtSg1yWkcbMZRxNAzt3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgt/yV1shK/y6tWwdrFHbuktQgw12SGmS4S1KDXHM/y610HVjSbLBzl6QGGe6S1CDDXZIatGy4J7ktyfEkjw2NfSDJN5M83H1cO/TYrUkOJXkiydWTKlyStLQ+nfungGsWGf9wVV3WfdwDkOQSYDtwafecjyQ5Z1zFSpL6WfZqmaq6P8l8z6+3Dbizqp4DnkxyCLgc+PLqS5Smk1caaZqNsuZ+c5JHumWb87uxTcDTQ8cc6cZeIMmOJPuS7Hv22WdHKEOSdLrVhvtHgVcClwHHgA9241nk2FrsC1TV7qpaqKqFubm5VZYhSVrMqsK9qp6pqpNV9TzwcQZLLzDo1DcPHXoRcHS0EiVJK7WqcE+ycejudcCpK2n2AtuTnJvkYmAr8OBoJUqSVmrZE6pJ7gCuBDYkOQK8H7gyyWUMllwOA+8EqKoDSfYAjwMngJuq6uREKpckLanP1TJvW2T4k2c4fiewc5SiJEmj8R2qktQgd4WUZox/oUl92LlLUoPs3KXGnemdtHb77bJzl6QG2blLjXCvGw2zc5ekBhnuktQgw12SGuSa+1nC9Vjp7GLnLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoPcz70x7tsuCezcJalJhrskNchwl6QGGe6S1CDDXZIatGy4J7ktyfEkjw2NvTzJvUm+3n0+f+ixW5McSvJEkqsnVbgkaWl9OvdPAdecNnYLcF9VbQXu6+6T5BJgO3Bp95yPJDlnbNVKknpZNtyr6n7gO6cNbwNu727fDrx5aPzOqnquqp4EDgGXj6dUSVJfq11zv7CqjgF0ny/oxjcBTw8dd6Qbe4EkO5LsS7Lv2WefXWUZkqTFjPuEahYZq8UOrKrdVbVQVQtzc3NjLkOSzm6rDfdnkmwE6D4f78aPAJuHjrsIOLr68iRJq7HacN8L3NDdvgG4e2h8e5Jzk1wMbAUeHK1ESdJKLbtxWJI7gCuBDUmOAO8HdgF7ktwIPAW8FaCqDiTZAzwOnABuqqqTE6pdkrSEZcO9qt62xENXLXH8TmDnKEVJWhtL7SJ6eNeb1rgSjZvvUJWkBrmfu6QXsKOffXbuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBbvkrqTe3Ap4ddu6S1CA79xm0VPckSafYuUtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkNsPTDG3GZC0WnbuktSgkTr3JIeB7wMngRNVtZDk5cBfAfPAYeDXq+q7o5XZNjt0SeM2js79DVV1WVUtdPdvAe6rqq3Afd19SdIamsSyzDbg9u727cCbJ/AakqQzGDXcC/jHJPuT7OjGLqyqYwDd5wtGfA1J0gqNerXMFVV1NMkFwL1J/q3vE7sfBjsAtmzZMmIZkqRhI3XuVXW0+3wc+CxwOfBMko0A3efjSzx3d1UtVNXC3NzcKGVIkk6z6nBP8qNJzjt1G/g14DFgL3BDd9gNwN2jFilJWplRlmUuBD6b5NTX+cuq+lySrwJ7ktwIPAW8dfQyJUkrsepwr6pvAK9eZPzbwFWjFCVJGo3bD0ga2VJvxDu8601rXIlOcfsBSWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CAvhZQ0MV4iuX7s3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDXua+hpa75laRxs3OXpAYZ7pLUIMNdkhrkmvsEuLYuab0Z7pKmhhuNjY/LMpLUIMNdkhpkuEtSg1xzl7TmvOhg8uzcJalBdu49eAZf0qyxc5ekBtm5S5pZ/la9NMN9BJ4UkjStXJaRpAbZuUs6653pt/BZXeKZWLgnuQb4E+Ac4BNVtWtSrzUuLrNI08n/N1duIuGe5Bzgz4FfBY4AX02yt6oen8TrSdKkzOpJ20l17pcDh6rqGwBJ7gS2ARMJ91n9jy9pba3nbwBrnVOpqvF/0eQtwDVV9dvd/euB11XVzUPH7AB2dHd/Cnhi7IWMbgPwrfUuYoycz3RraT4tzQWmdz4/UVVziz0wqc49i4z9v58iVbUb2D2h1x+LJPuqamG96xgX5zPdWppPS3OB2ZzPpC6FPAJsHrp/EXB0Qq8lSTrNpML9q8DWJBcneQmwHdg7odeSJJ1mIssyVXUiyc3APzC4FPK2qjowideasKleNloF5zPdWppPS3OBGZzPRE6oSpLWl9sPSFKDDHdJapDhzmCrhCRPJDmU5JZFHk+SP+0efyTJa9ejzr56zOc3u3k8kuRLSV69HnX2sdxcho77+SQnu/dYTK0+80lyZZKHkxxI8i9rXeNK9Pi39mNJ/jbJ17r5vGM96uwjyW1Jjid5bInHZyoHqKqz+oPBCd//AH4SeAnwNeCS0465Fvh7Btfvvx74ynrXPeJ8fgE4v7v9xmmdT5+5DB33T8A9wFvWu+4RvzcvY/BO7i3d/QvWu+4R5/M+4A+723PAd4CXrHftS8znl4HXAo8t8fjM5EBV2bkztFVCVf0PcGqrhGHbgL+ogQeAlyXZuNaF9rTsfKrqS1X13e7uAwzehzCN+nxvAH4P+AxwfC2LW4U+8/kN4K6qegqgqqZ5Tn3mU8B5SQK8lEG4n1jbMvupqvsZ1LeUWcoBwx3YBDw9dP9IN7bSY6bFSmu9kUE3Mo2WnUuSTcB1wMfWsK7V6vO9eRVwfpJ/TrI/ydvXrLqV6zOfPwN+hsGbGB8F3lVVz69NeWM3Szngfu702Cqh5zHTonetSd7AINx/caIVrV6fufwx8N6qOjloDqdan/m8CPg54Crgh4EvJ3mgqv590sWtQp/5XA08DPwK8Erg3iT/WlXfm3BtkzBLOWC402+rhFnaTqFXrUl+FvgE8Maq+vYa1bZSfeayANzZBfsG4NokJ6rqb9akwpXp+2/tW1X1A+AHSe4HXg1MY7j3mc87gF01WLQ+lORJ4KeBB9emxLGapRxwWYZ+WyXsBd7enS1/PfBfVXVsrQvtadn5JNkC3AVcP6Ud4SnLzqWqLq6q+aqaB/4a+N0pDXbo92/tbuCXkrwoyY8ArwMOrnGdffWZz1MMfgshyYUMdoD9xppWOT6zlAN27rXEVglJfqd7/GMMrsK4FjgE/DeDbmQq9ZzP7wM/Dnyk63hP1BTueNdzLjOjz3yq6mCSzwGPAM8z+Ctmi16at956fn/+APhUkkcZLGu8t6qmcetcktwBXAlsSHIEeD/wYpi9HAC3H5CkJrksI0kNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg/4Xpj4QhAUVgzUAAAAASUVORK5CYII=",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.hist(df['log10000'],bins=50)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Average 0.4443985447251986\n",
+      "Variance 0.03232000955459355\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = np.array(df['log10000'])\n",
+    "m1 = np.average(x)\n",
+    "ss = np.var(x,ddof=1)\n",
+    "print(\"Average\", m1)\n",
+    "print(\"Variance\", ss)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Alpha MME :  2.950580908925828\n",
+      "Beta MME :  3.688911825575294\n"
+     ]
+    }
+   ],
+   "source": [
+    "#From method of moments\n",
+    "alphaMM = m1*((m1*(1-m1)/ss)-1)\n",
+    "betaMM  = alphaMM*(1-m1)/m1\n",
+    "print(\"Alpha MME : \", alphaMM)\n",
+    "print(\"Beta MME : \", betaMM)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Plotting fit on density histogram\n",
+    "\n",
+    "fig,ax = plt.subplots(1,1)\n",
+    "ax.hist(x,density=True,bins=100)\n",
+    "xx = np.linspace(0,1,50)\n",
+    "ax.plot(xx, st.beta.pdf(xx,alphaMM,betaMM),label=\"Beta fit MM\")\n",
+    "ax.legend(loc='best')\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Use bootstrap method to find alpha and beta\n",
+    "\n",
+    "N= 1000 #Running the simulation 1000 times\n",
+    "n = 5000 #As we have 5000 samples\n",
+    "alpha_hat = np.zeros(N)\n",
+    "beta_hat = np.zeros(N)\n",
+    "for i in np.arange(N):\n",
+    "    xi = st.beta.rvs(alphaMM,betaMM,size=n)\n",
+    "    m1i = np.average(xi); ssi = np.var(xi)\n",
+    "    alpha_hat[i] = m1i*((m1i*(1-m1i)/ssi)-1)\n",
+    "    beta_hat[i]  = alpha_hat[i]*(1-m1i)/m1i\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([0.10135004, 0.10135004, 0.20270007, 0.40540014, 0.30405011,\n",
+       "        0.50675018, 0.91215032, 0.50675018, 1.01350035, 1.62160056,\n",
+       "        1.01350035, 1.82430063, 2.22970077, 1.62160056, 3.95265137,\n",
+       "        3.54725123, 4.0540014 , 3.04050105, 5.16885179, 4.96615172,\n",
+       "        5.57425193, 4.86480168, 5.16885179, 6.18235214, 5.776952  ,\n",
+       "        5.776952  , 5.57425193, 3.54725123, 3.14185109, 2.93915102,\n",
+       "        2.53375088, 2.63510091, 2.0270007 , 2.33105081, 0.81080028,\n",
+       "        1.41890049, 1.01350035, 0.91215032, 0.50675018, 0.40540014,\n",
+       "        0.20270007, 0.10135004, 0.40540014, 0.10135004, 0.10135004,\n",
+       "        0.        , 0.10135004, 0.        , 0.        , 0.10135004]),\n",
+       " array([3.46739117, 3.47725796, 3.48712476, 3.49699155, 3.50685835,\n",
+       "        3.51672514, 3.52659193, 3.53645873, 3.54632552, 3.55619232,\n",
+       "        3.56605911, 3.57592591, 3.5857927 , 3.5956595 , 3.60552629,\n",
+       "        3.61539309, 3.62525988, 3.63512668, 3.64499347, 3.65486027,\n",
+       "        3.66472706, 3.67459386, 3.68446065, 3.69432745, 3.70419424,\n",
+       "        3.71406104, 3.72392783, 3.73379463, 3.74366142, 3.75352822,\n",
+       "        3.76339501, 3.7732618 , 3.7831286 , 3.79299539, 3.80286219,\n",
+       "        3.81272898, 3.82259578, 3.83246257, 3.84232937, 3.85219616,\n",
+       "        3.86206296, 3.87192975, 3.88179655, 3.89166334, 3.90153014,\n",
+       "        3.91139693, 3.92126373, 3.93113052, 3.94099732, 3.95086411,\n",
+       "        3.96073091]),\n",
+       " <BarContainer object of 50 artists>)"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 432x288 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Plot histogram of the estimates(alpha,beta) from bootstrap\n",
+    "\n",
+    "ax1 = plt.subplot(121)\n",
+    "ax1.hist(alpha_hat,density=True,bins=50)\n",
+    "ax2 = plt.subplot(122)\n",
+    "ax2.hist(beta_hat,density=True,bins=50)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The sample standard deviations of the estimates is a bootstrap estimate for the standard error of the estimator"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.06084364592865924\n",
+      "0.07449059421438306\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(np.sqrt(np.var(alpha_hat)))\n",
+    "print(np.sqrt(np.var(beta_hat)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.11831024834220828, -0.12187918873784653]\n",
+      "[0.14758773972765935, -0.15128779226763694]\n"
+     ]
+    }
+   ],
+   "source": [
+    "del1_alpha = np.percentile(alpha_hat - alphaMM, 97.5)\n",
+    "del2_alpha = np.percentile(alpha_hat - alphaMM, 2.5)\n",
+    "print([del1_alpha,del2_alpha])\n",
+    "del1_beta = np.percentile(beta_hat - betaMM, 97.5)\n",
+    "del2_beta = np.percentile(beta_hat - betaMM, 2.5)\n",
+    "print([del1_beta,del2_beta])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[2.8322706605836196, 3.0724600976636744]\n",
+      "[3.5413240858476347, 3.8401996178429307]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#The 95% C.I. works out to(for alpha and beta):\n",
+    "print([alphaMM - del1_alpha, alphaMM - del2_alpha])\n",
+    "print([betaMM - del1_beta, betaMM - del2_beta])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Using MLE:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3.0393044178574136\n",
+      "3.791020430224173\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Referred wiki for formulae for estimation of alpha and beta\n",
+    "\n",
+    "p = np.sign(x) * (np.abs(x))**(1/n)\n",
+    "pminusx = (np.abs(1-x)**(1/n))\n",
+    "G_x = np.prod(p)\n",
+    "G_1minusx = np.prod(pminusx)\n",
+    "\n",
+    "alphaML = 1/2 + G_x/(2*(1 - G_x - G_1minusx))\n",
+    "print(alphaML)\n",
+    "betaML = 1/2 + G_1minusx/(2*(1 - G_x - G_1minusx))\n",
+    "print(betaML)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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mb5/OnB1zTKcS4lek0IXPFFQUMGrJ/bRyOjnv4LlMc19uOpJvtRsAV4zlr99v4iJ7ImPWjWFD9gbTqYT4hazlInxCa83fl/2V/KoiRmbHMNp5O8Fygeajz2DdO+YOrEUHeH7VS9zYpj1/WfYX5gyYQ1pUmsGEQlSTQhe1+nWJ1b2U7PvbZ/JF9jr+WuLinyX34/Kjf1r13Zc6XfIYsQU/MW7HXG5smc4DSx9gWv9phFnD6n6sEA1IDrmIU6bsOTy39gUuKKvgswO3kUOQr1KoFAx6hTZNOvPc4Vy25W3jpcyXTKcSQgpdnCoPzU+bgkO7aXmoG2s855oO1DjsDvjDDPqoaIaXe5i5YyaL9i4ynUqEOCl0cUpSEhdREHmEwXkOplbeYDpO44ppAkNn8kBuLufpMJ786kn2FcmSu8IcKXRRp5+Xtj12eVurPQdPyjK6l1Xxbt6f8ITiP6emHbEP+Ddjs37A4qrkweUP4nQ7TacSISoE/wcK39C0Pu0NwrUHdfAKDpJiOpA5nYZyWufbePrQAb7N+5YJmyb8ctfxfhgK0RCk0MVJaR63mOzIIvrkJbCwqq/pOOZd9jx9Es/lutJKpmybwrqD60wnEiFICl3Um9VajKfJF5xT4eKjvHtNx/EPtjAYPIWHiytp5VGMXjGawspC06lEiPGfycIiYJzb5E1+tGgcB/tRQJzpOKfEV4dCfn6efpbbecH9CsOaaZ5b+xxwkU+eXwhvyAhd1EuzyA3sicumV0EUyyouNR3H73zuyaB95zu5+8gRPvnhE2wxW01HEiFECl3Ug5u4Ju+T6nKzOvtuguXUfp/r9xR3OFpyjtNNRNpclLXYdCIRIqTQhdcyEt5hn8NDi5wO5OompuP4L1s49msn84/cAmyWcsKbzgO06VQiBMgxdOGVGEsuh1K+5qxyC8sLbjQd56Q12vTB1LNpc8lT3L/yKV5K+hZX7BZgQOO8tghZUujCK+enTuZriyLy0LV4sJqOUyu/m+vd5U6af/Q250Rl822TeeRXjCTRkWg6lQhicshF1Klt+Ca2xOdzblEC31V0NR0ncCjFaOcIHs4px2KtYMza500nEkFOCl3UQZOW+i5hGrZm3246TMDJIYEpZTdzd0EBn+79jGX7lpmOJIKYFHqIq+vU9J5RH/N1tJsW+WdQ7E5t5HTBYYGnO03z2nFmlZNnv3qSUmep6UgiSEmhi+NyUE556pckumBj7nDTcQLaU87beLLEw+HyfF7ZMM50HBGk6ix0pdQUpdRhpdS249zfWylVqJTaVPPxhO9jChP6xb/Ndw4rYTk98GiH6TgB7QixdLzsRW4oLmbmzllYHLLMrvA9b0boU4G6rva7Qmvdqebj6VOPJUxLIZfdyd+RVmljV4EPLtsmoP1V3J/agxSXm7imcwC36UQiyNRZ6Frr5UB+I2QRfqR34lSy7DaKD1+JHJnznZgrX2Z0cRUuRy5hiatMxxFBxlf/U7srpTYrpT5VSp1zvI2UUiOUUplKqcycnBwfvbTwtYoDm9iQdIim5REcKulmOk5wiU6lT+9n6VVWTlTKQpRNVmQUvuOLQt8ItNJadwReAT443oZa60la6wytdUZKSghfEMHPzVr8F3JsNrKzByPrtfie6vgH+hxOxYKL+CZzTccRQeSUC11rXaS1Lqn5/BPArpRKPuVkwojiXQuZ7DpE09IECsuP+8uWOBVK8XLFXdxWUIordierslaaTiSCxCmf+q+USgOytdZaKdWV6h8SeaecTDQ+rZm+/AkKbVZyD//BdBq/dypLDWTpVPLyLiM9ehnPrfwb867/nDBrmA/TiVDkzbTFWcBq4CylVJZS6g6l1Eil1MiaTQYD25RSm4HxwBCttSwtF4CKtr3H26qES2LPoKIi3XScoPeW6wqG5obxU2U+b22eBMg1SMWpqXOErrUeWsf9rwKv+iyRMMKCh7fXPEdxmIV7ez3L/LV7TUcKem6szC66kz5x45i09U0GnDXYdCQR4GS1RQHAANtSptuqSCpuxmVj95qOE9DqM7reotswsUV/BuUuZeyKvwHXNlwwEfRkgrHAjosmSZ9QYrGwL0dGiY3ttH7/4M5yDwuz12GL3GU6jghgUuiCQfbFfBRvJb64Be7KZqbjhB5HHLf1fJJmThdN0mYjZ5CKkyWFHuLCcJKauIhSi4X9OdeYjhOS0kd9zFkzo7kyN4ai8FISEpaZjiQClBxDD3HX2BfzYZyV2OLmFFeeZjqO32j8WSaKuYV30iX+RbamfAFFcoauqD8ZoYcyZwVpCYsoslo5mHuV6TQh7wfdjPTDnXBa3LRIecd0HBGApNBDWFnmm8yLtxFdchqeiham4whgZtlQrihyURi/g+9yt5uOIwKMFHqoclXy/sbXOGK1cjh3oOk0okYF4Rw8fC0xHg//XPoXfj5HT044Et6QY+ghyrlxGtMcmqiyVIrLW5uOI46y1HUht+Uv5j1rFuf/42mOlGSYjiQChIzQQ5GrigXrx5Nts5GTKxev8D+KZXm307rKSWyTDwCX6UAiQEihhyD35plMCXPRLqoZ7tK2puOIWvygW3BOTlvyw1y0TppvOo4IEFLoocbtYsnaf7E3zM7tv/szst65/5pfdAtdylyUJa1HWYtNxxEBQAo9xOht7zPZVkErRzL9WvUzHUecQBkOLNl9qLRo2qe+bTqOCABS6KHE42Ht6rF8Ex7OrZ3uxWqxmk4k6rC44nJ+X2QjK+5HYsJ+NB1H+Dkp9FDy3adM1UdIskUx8IxBptMIryh2Hh5GlEeTniajdHFiMm0xRKSPWsC46MdZ1SKC+8+9jXBruOlIwks7XO25Kj+FJSl5tIhaDdRvZtLRc9f3jpFZTcFMRughorvlW9YkFGL1WLn+7CGm44h6Wp53B6c53UQ2WYDbI6sxitpJoYeIIeHz+CQqkqojXYkLjzMdR9TTEZ1Iq5xzORDuZv6q50zHEX5KCj0UHPianQkH0CjK839vOo04SUsLb+SsCg+v7n6HsvIC03GEH5JCDwFFK1/ivZhodNF5aFe86TjiJDmxQ/al5Fhg6uL7TccRfkgKPdjl7+H9/V9SbrFQmtfbdBpxijLL+nKpimFq7gYO5+4wHUf4GZnlEuScq8YxIzYGS2lLPHJ5uaDw54vGsGTZvUxYfD/TNv1frdvIbJbQJCP0YFZymIXfzSPbZqUk/xLTaYSPtEi/iBsjT2dexX7aODaajiP8iBR6ENNrX+etmAhaRzXDXSKLcAWTEZe+QoyG5NT3AW06jvATcsglWFWVsn7LVLYnRvJkhzt5MPN/P7vlIgmBLy6+FXenXcSLh1fQNXoB60p+fZES+R6HJhmhB6tNM3k7HBLs0Qw4fYDpNEHDn64cNKTPWJo4NeWpKwij0nQc4Qek0IORx82Pa1/hy8hIbmg3DIfNYTqRaABhYZE4cnqyN9xCr4TppuMIPyCHXILR9o+YThE2SzxD5DR/v9EQo/pthQM4N3Ete5J3kFiQQ75O8flriMAhI/RgozWFX41jfkwM/VtfQXJEsulEokEpCrOvJtdmpXvyf02HEYbJCD3Y7FvLeyW7KE9M4OZzbjGdRjSAY0f6+8oy6FSykMzEXNoe2c53rnaGkgnTZIQeZJyrxjMrLo6uqb/jrMSzTMcRjeT77JuoVIozU2cg0xhDV52FrpSaopQ6rJTadpz7lVJqvFJqt1Jqi1LqfN/HFF7J+54vspaSbbUw/NxbTacRjai4qhWtClqwKtZJD8dS03GEId6M0KcCl5/g/v7AmTUfI4D/nHoscVLWTuTtuFhaRJ3GRc0vMp1GNLJtOTcT7oHw1E8Jw2k6jjCgzkLXWi8H8k+wyVXAW7raGiBeKdXUVwGFl8ry2fLNbLaEhzHsnJuxKDmaFmrc7lji8zuxPsrK5dFzTMcRBvjif30zYN9Rt7NqvvYbSqkRSqlMpVRmTk6OD15a/GLDVKZH2om2RXD1GVebTiMM2Zk3mASnhf2pX5NIgek4opH5YpaLquVrtb4ro7WeBEwCyMjIkHdufMVVxaHMSXyeGMWNba8nyh7lF2cyCgO0HXdOX747bREDEv7LrCMPmE4kGpEvRuhZQIujbjcHDvjgeYW3vpnHHEsZHhRDzx5qOo0wbH9hb5pUOFifvJ+2lu9NxxGNyBeF/iFwc81sl25Aodb6oA+eV3ghfdQCNsz9B3NiYrm4xcU0j2luOpIwzsLhQ9eTbbPRNXkax5vG6E/r0gjf8Gba4ixgNXCWUipLKXWHUmqkUmpkzSafAHuA3cAbwL0Nllb8Rle1g70xuRRbFcPa32Q6jvATReXn0LQkmc8TKrjYvtJ0HNFI6jyGrrU+4e/wWmsN3OezRKJe7rB9zIS4ODwVaVz/72xARlui2p7s4USf/i+SU+YTdqAbVdhNRxINTOa2BbK874mN/JYfwmxU5vek9venRahyVTUhoeBsFsVauTbiPdNxRCOQQg9kaycyPS4GXJG4ijqaTiP80N6cGwjzWMhLXUeKTGMMelLogaq8gH1bZrE8MoLKgm6g5ddp8VvaHYUlrydrIsO5Jnaq6TiigUmhB6qN05gZaQUsOI90M51G+LHs/MuIrQpjfcpPuPatNx1HNCBZPjcQuV2UrJvEvIQ4nEUd0K5Y04mEP9M2Cg8Poqj5e8z9/M/ccNtKUL9+v+XYqYt7x1zZmAmFj8gIPRBt/5D5uoBSpanK72E6jQgAJcW/I6EsgQkcoXiTXK4uWEmhByDPmgnMjE+kQ3IHPBUt6n6AECj2Z9/IEYuVN9aMgapS04FEA5BCDzT71rMybxs/WeEmOZFI1IO7ogUDm17I9AjFvqVPmY4jGoAUeqBZM4Hp8QmkRiTTt1Vf02lEgLm/1zPYlJWX98yjpco2HUf4mBR6ICnYx+5dn7DaYWdou2HYLTJVUdRPamQqd7S/mc8jHQyNmWI6jvAxKfRAsu51ZsRGE24JY/CZg02nEQHqls73cZotmi+Sc7jI8rXpOMKHpNADRWUJBRvf5qOYaAa0GUi8I950IhGgHDYHf+n2GDvDw+iWMEMuVxdEpNADxaYZvBfuoRLNsHbDTKcRAe7S068guiyF2UmK4faPTMcRPiKFHgg8bpxrJjArIZFuTbtxZsKZphOJAKeUIvvQEAosVlTKUpqSZzqS8AEp9ECw81MWV+VwWHm4qZ1MVRS+4alshr2gA+/FRnJn1H9NxxE+IIUeAPTqV3k7MZlWMS3p1byX6TgiiOTnXIXVY2N1ShYXWraYjiNOkRS6v9u/kc3ZG9hqg2Htb8Ki5FsmfEe7oyjLuZy1EQ76x72FHZfpSOIUSDv4uzWv8XZ8IjH2GK5qc5XpNCIIlR+5kIjKON5OhttsH5qOI06BrLbozwr3c2DHhyxu3oRb2g4m0h5pOpEISlbyDg6hPP11HMlLaJ7d81erL8rKi4FDRuj+bO1EZsVEopSFG9vdaDqNCGLu8tbYCtszPT6KeyPkDdJAJSN0f1VZTOnGabzfNJG+rfqSFpX2y13Hrl0thC8UZF9DQvROlqccoN++dXzu6Qogo/UAIiN0f/X1dOaFeSjGzc3tbzadRoQA7Y6hNOcyVkVG0C9uBlGUm44k6klG6P7I7cK15jWmJybTObUDHVI6mE4kgkRdv91VHulBdPwaJiUf5o8lc3jBeWvjBBM+ISN0f7TjI5ZU5bBfubml/S2m04iQYuXIwSFkW20UJ6/nXLXHdCBRD1Lo/kZrWDWeaUkptIhpQe8WvU0nEiHGU9ESCs5nRlw0I6PewIrbdCThJSl0f/PjKjblbWOLDYa3H47VYjWdSISg4sMDsLrDmZVSwW3WT0zHEV6SQvc3q8YzLTGZ2LBYOZFImOOJpCj7arY4wmmZ+Klc3ShASKH7k8M72PvDF3zhsPGHs/4gJxIJo1xFnbGUpDMhMZqHwycBmvRRH//yIfyPFLo/+eoV3kpIwG6xy4lEwg8oig5dTwU2FqbmMNi6zHQgUQcpdH9RdJDcbe8yPzqKQWdcRXJEsulEQqCdSZTnXMqyqEh6xb1Lmqyb7te8KnSl1OVKqZ1Kqd1KqVG13N9bKVWolNpU8/GE76MGr/RRH/P6P//KzGgHTrRMVRR+pSq/F9aKVP6VFMXfwt8AtOlI4jjqPLFIKWUFJgD9gCxgvVLqQ631t8dsukJrPaABMga9WEq4xraEAbGpVBW1p/fz3wDf/Oo0azlmKcyxUnRgCJ7Wr/BV6n6u27+C9z0XmQ4lauHNCL0rsFtrvUdrXQXMBmT6hQ8Nty7ms1gb5VZNVb78RxH+x1N5GpW5F7MgOoo+cbNoQr7pSKIW3hR6M2DfUbezar52rO5Kqc1KqU+VUufU9kRKqRFKqUylVGZOTs5JxA1CVWUMs33GpLhEXKWn4ylvZTqRELWqzL0Ea0USY5OjeSp8YvVJcMKveFPoqpavHfud3Ai00lp3BF4BPqjtibTWk7TWGVrrjJSUlHoFDVqbZrA6xk2hTVOV19t0GiFOwEbRwaHkWm18mXoQMiebDiSO4U2hZwEtjrrdHDhw9AZa6yKtdUnN558AdqWUTNOoi9uJe9V4XotLxl3eDHfpmaYTCXFCnormVNQcelm8/BnI+950JHEUbwp9PXCmUqq1UioMGAL86jpVSqk0pZSq+bxrzfPK/Ka6bJnD565cDof9PDqv7ZchIfxLVW4fVHkTnk6IJnfuneB2mo4katRZ6FprF/BHYCGwHXhHa/2NUmqkUmpkzWaDgW1Kqc3AeGCI1nKA7YTcLjwrxvJGchPclSm4imt920EIP2Sl5MCNlNrCeMr5E3rZGNOBRA1lqnczMjJ0Zmamkdf2C1ve5YvP/sSfm6RQvv8GXEXnm04kRL08PTyPFzNf5PG8I9xw3TvQ6kLTkUKCUmqD1jqjtvvkTFETPB70ihd5PbkJLWNa4irqaDqREPV2U/ubuDCtKy8mJrDng7ug/IjpSCFPCt2E7R/yZclPbLd6uKvDXYAskSsCj0VZeLbXGCLCYng40k3VB/fKVEbDpNAbm8eDXvY8/0lJpXl0cwacLifXisCVEpnCM72eZ2eYnZdyVsPa101HCmlyTdHG9u08VpTs5dvoVJ7uMAKbRb4FIjAdvRzFvdcO5+3tb5Ox8ln6tegCzX5nMFnokhF6Y/K48Sx7nldT0vBUJfLAZKus0SKCwgO/e4DzEtvxRFI8+96/FcpkaQATpNAb07b3+bwsi+1WD5U5fZFj5yJY2K12Xrz4ZVRYFH+NcFL53u3gkWuRNjYp9MbiduFe9jwTUprQJu50XEWdTCcSwqeaRTfjuYteYHuYnWeKNqOX/MN0pJAjhd5Yvn6bBVXZ/GDx8MfOf0L+6kUw+fmydLdOKGVkh7uZHxPNnM2vw/YFpqOFFGmVxlBVRtWyMfw7vnrNljv/U2E6kRAN5p5O9/L703ryQlIiGxfcC4e2mo4UMqTQG8Pa/zDLUkquXVOZczmyZosIZhZl4bnfv0Cz6GY8kBxL1pyhUHLYdKyQIIXe0MryKVg1jteTknCVtJUVFUVIiA2L5dV+EynQDu6NdLFibH9wym+mDU0mQTe05WN5PdJCKZrKw1eYTiNEgzt6Kq41cjh7W05mRpNCur9/J7YbpoFFZnc1FBmhN6TcXfy08U1mx8VyzZnX4qlMM51IiEblLjuD8kPXsCoygqdzV6E/fUSWB2hAUugNaeHfGJuYiN0azn2d7jOdRggjnAVdqcy5hHkx0byy+x1Y9W/TkYKWFHpD2bWY5VlfsjTCzoiOd5MSKZfcE6GrKrcf151xHW/ExzFj3VhY/6bpSEFJjqE3BLeTyoWjGJOSSnpsK25pf4vpREIYpnis+2MUVOYzhqU4vnyC6+yR0OlG08GCiozQG8LqCUxxZbPPCo9e8DfsVrvpREIYZ7PY+Ofvx9Kz6YU8lZLEh4sfgq3vmY4VVKTQfS3/B/at+CeTExK4LP0yup/W3XQiIfxGmDWMly8ZxwVNuvB4ciIfLbwfNs0yHStoSKH7ktZ4FjzA40mx2G0RPJTxkOlEQvgdh83B+L4T6JKWwaMpicz54kHYMNV0rKAghe5LW99jVu56NoTbyfmpPxc8E8LXTBXiBNo9toTFX16Fp/gsnk1O5M3lj6O/fFGmNJ4iKXRfKc5m3+ejGJeYiKukLa7CWq/hKoT4mbZTmnUz7sIOjEuM5x9bJuBa8IAsu3sKpNB9QWtcH9zDY9E2rPZIKg5eh6zXIoQ3rJQdGEJVXi/mxMbwp6wFlM68ASoKTQcLSFLovrBuEq/lZ7LREUbOjwPRrjjTiYQIIBYqD19JxcGrWR0ZybDyb/hh8sWQu8t0sIAjhX6qDm9nxYpneSM+jqojXXAVdTadSIiA5CzoRvGPt7PXEs2QyCoWv30ZfDPPdKyAIoV+KsqPcHDOUEYnxaEqUqnMHmQ6kRABzV12JoU/PEBFZVMeSIzi2SUPUDb/XqgqNR0tIEihnyy3i+J3b+E+RwUuewTF+4eDlhOIhDhV2hVP4Y9/5JZ2w3knNobrc5aw6Y0esHeV6Wh+TwrdCz9fXuvoZUGrPn+MP5dt54ewcF6+ZDy6StZqEcJntI0Huz7M5Mum4Ipuws1Rbp7+aBiFH/4RygtMp/NbspbLcRxd3sdyr3iJx75/h3XRUTzX89mas0Fr3/5EzyOEOLEuaV2Ye90nvLZhHDN2zmZx7hLufaML13X9C/Yud4Isq/ErUuj19MxjI8g97QuWREfxwPn3M7DNQNORhAhqUfYoHur2KIPaXsfzKx/jH9YdTN02nutWjOebIwNY4OmJCxt7x1xpOqpxcsjFSwoPI+zvsrvFUpZGRlJ16EpuP+9O07GECBlnJZ7Ffwe+Q9lPt3LEncz4VBtb2yzg3tRHGGb/EMqPmI5onIzQvRBLCffEvMKHTXI5aHNQsf8PVBV3lsMpQtSDL/6/KKVwl55N9g8PY43eSXnip/w36TD2xFWUT+3KgMSO9Oh0O+Ft+oItzOs8wTK6V9qLtROUUpcD4wAr8KbWeswx96ua+68AyoBbtdYbT/ScGRkZOjPT/Fonx/umpo/6GIWHi+2raJo8nw/jbURVOcg5cAvu8tYmogohamEJP0Ba/FLsSTvI104cHg8XVLnpEduGTi0u4syzrsGWfCaoX5+9fbwfMP5e7kqpDVrrWtcWqbPQlVJW4DugH5AFrAeGaq2/PWqbK4A/UV3oFwDjtNYXnOh5T6XQffmT9dhvajjltAr7jmaOHYTHbmRdNDiVIi6/PVmHh4A+8U99IYQZu567lLX7VrB8xzssz97Afl0BQITHQ+sqN3FVEVzQtA1psS1IjT+dxz/Op9idQJE7iQodiRM7dS3ZcSp946veOlGhe3PIpSuwW2u9p+bJZgNXAd8etc1VwFu6+qfDGqVUvFKqqdb64EmnNuCi1HFsSTzAQaU4CES6IbXgdHbnD6K4qqnpeEKIE7Bb7PRsdQk9W13CaK05ULKfzXsWMnHp+5SG57A/soLVpTuhdCccBE7/32MdQJTW2DQoNAo4uzCZ5YceNrQ3J8ebEfpg4HKt9Z01t4cDF2it/3jUNguAMVrrlTW3vwAe0VpnHvNcI4ARNTfPAnb6akd8KBnINR3Ch2R//Fcw7QvI/jSWVlrrWk988WaEXtvvIMf+FPBmG7TWk4BJXrymMUqpzOP9OhOIZH/8VzDtC8j++ANvpi1mAS2Out0cOHAS2wghhGhA3hT6euBMpVRrpVQYMAT48JhtPgRuVtW6AYWBdvxcCCECXZ2HXLTWLqXUH4GFVE9bnKK1/kYpNbLm/onAJ1TPcNlN9bTF2xoucoPz60NCJ0H2x38F076A7I9xXs1DF0II4f/k1H8hhAgSUuhCCBEkQrbQlVKXK6V2KqV2K6VG1XK/UkqNr7l/i1LqfBM5veXF/gyr2Y8tSqmvlFIdTeT0Rl37ctR2XZRS7ppzJfyWN/ujlOqtlNqklPpGKfVlY2esDy/+rcUppT5SSm2u2R+/fU9NKTVFKXVYKbXtOPcHVA+gtQ65D6rf3P2e6nPFwoDNQPtjtrkC+JTqOfbdgLWmc5/i/lwIJNR83t9f98ebfTlquyVUvyE/2HTuU/zexFN95nXLmtuppnOf4v48CrxQ83kKkA+Emc5+nP25CDgf2Hac+wOmB7TWITtC/2U5A611FfDzcgZH+2U5A631GiBeKeWv5//XuT9a66+01j+vL7qG6nMF/JE33xuoXjvofeBwY4Y7Cd7sz43AXK31TwBaa3/eJ2/2RwMxNYv2RVNd6K7GjekdrfVyqvMdTyD1QMgWejNg31G3s2q+Vt9t/EV9s95B9ajDH9W5L0qpZsA1wMRGzHWyvPnetAUSlFLLlFIblFI3N1q6+vNmf14F2lF9cuFW4H6ttadx4vlcIPVAyK6H7rPlDPyE11mVUhdTXeg9GzTRyfNmX/5N9VpBbqVOvDqeH/Bmf2zA74A+QASwWim1Rmv9XUOHOwne7M9lwCbgEqAN8LlSaoXWuqiBszWEQOqBkC30YFvOwKusSqkOwJtAf611XiNlqy9v9iUDmF1T5snAFUopl9b6g0ZJWD/e/lvL1VqXAqVKqeVAR6qXrfY33uzPbVQv1qeB3UqpH4CzgXWNE9GnAqkHQvaQS7AtZ1Dn/iilWgJzgeF+OvL7WZ37orVurbVO11qnA+8B9/ppmYN3/9bmA72UUjalVCTV1xTY3sg5veXN/vxE9W8bKKWaUL2y6p5GTek7gdQDoTlC10G2nIGX+/MEkAS8VjOydWk/XEnOy30JGN7sj9Z6u1LqM2AL4KH6qmC1TqMzzcvvzzPAVKXUVqoPWTyitfbHZWhRSs0CegPJSqks4EnADoHXAyCn/gshRNAI1UMuQggRdKTQhRAiSEihCyFEkJBCF0KIICGFLoQQQUIKXQghgoQUuhBCBIn/BwCw2YWATKiqAAAAAElFTkSuQmCC",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Checking the fit with the histogram\n",
+    "\n",
+    "fig,ax = plt.subplots(1,1)\n",
+    "ax.hist(x,density=True,bins=100)\n",
+    "xx = np.linspace(0,1,100)\n",
+    "ax.plot(xx, st.beta.pdf(xx,alphaMM,betaMM),label=\"Beta fit MM\")\n",
+    "ax.plot(xx, st.beta.pdf(xx,alphaML,betaML),label=\"Beta fit ML\")\n",
+    "ax.legend(loc='best')\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "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>Sno</th>\n",
+       "      <th>Order ID</th>\n",
+       "      <th>Date of placing order</th>\n",
+       "      <th>Order Dispatch date</th>\n",
+       "      <th>Logistics Type</th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Segment</th>\n",
+       "      <th>Country</th>\n",
+       "      <th>City</th>\n",
+       "      <th>State</th>\n",
+       "      <th>...</th>\n",
+       "      <th>Discount</th>\n",
+       "      <th>Profit</th>\n",
+       "      <th>Unnamed: 20</th>\n",
+       "      <th>log10000</th>\n",
+       "      <th>Total Sales</th>\n",
+       "      <th>Month</th>\n",
+       "      <th>Quarter</th>\n",
+       "      <th>Unnamed: 25</th>\n",
+       "      <th>Unnamed: 26</th>\n",
+       "      <th>Unnamed: 27</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>740</td>\n",
+       "      <td>CA-2014-112326</td>\n",
+       "      <td>2014-01-04</td>\n",
+       "      <td>2014-01-08</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Phillina Ober</td>\n",
+       "      <td>Home Office</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Naperville</td>\n",
+       "      <td>Illinois</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>4.2717</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.267823</td>\n",
+       "      <td>38127.933</td>\n",
+       "      <td>Jan</td>\n",
+       "      <td>Q1</td>\n",
+       "      <td>39360.06045</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>741</td>\n",
+       "      <td>CA-2014-112326</td>\n",
+       "      <td>2014-01-04</td>\n",
+       "      <td>2014-01-08</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Phillina Ober</td>\n",
+       "      <td>Home Office</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Naperville</td>\n",
+       "      <td>Illinois</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>-64.7748</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.608936</td>\n",
+       "      <td>21452.645</td>\n",
+       "      <td>Feb</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>742</td>\n",
+       "      <td>CA-2014-112326</td>\n",
+       "      <td>2014-01-04</td>\n",
+       "      <td>2014-01-08</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Phillina Ober</td>\n",
+       "      <td>Home Office</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Naperville</td>\n",
+       "      <td>Illinois</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.8</td>\n",
+       "      <td>-5.4870</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.137251</td>\n",
+       "      <td>97859.6638</td>\n",
+       "      <td>Mar</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1760</td>\n",
+       "      <td>CA-2014-141817</td>\n",
+       "      <td>2014-01-05</td>\n",
+       "      <td>2014-01-12</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Mick Brown</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Philadelphia</td>\n",
+       "      <td>Pennsylvania</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>4.8840</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.322709</td>\n",
+       "      <td>81724.5361</td>\n",
+       "      <td>Apr</td>\n",
+       "      <td>Q2</td>\n",
+       "      <td>55751.25475</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>593</td>\n",
+       "      <td>CA-2014-135405</td>\n",
+       "      <td>2014-01-09</td>\n",
+       "      <td>2014-01-13</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Melanie Seite</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Laredo</td>\n",
+       "      <td>Texas</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>1.1680</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0.242633</td>\n",
+       "      <td>70289.3068</td>\n",
+       "      <td>May</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4995</th>\n",
+       "      <td>907</td>\n",
+       "      <td>CA-2017-143259</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Patrick O'Donnell</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>New York City</td>\n",
+       "      <td>New York</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>12.1176</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.627346</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4996</th>\n",
+       "      <td>908</td>\n",
+       "      <td>CA-2017-143259</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Patrick O'Donnell</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>New York City</td>\n",
+       "      <td>New York</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>2.7279</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.489677</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4997</th>\n",
+       "      <td>909</td>\n",
+       "      <td>CA-2017-143259</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Patrick O'Donnell</td>\n",
+       "      <td>Consumer</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>New York City</td>\n",
+       "      <td>New York</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>19.7910</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.430609</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4998</th>\n",
+       "      <td>1297</td>\n",
+       "      <td>CA-2017-115427</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Erica Bern</td>\n",
+       "      <td>Corporate</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Fairfield</td>\n",
+       "      <td>California</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>4.5188</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.285785</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4999</th>\n",
+       "      <td>1298</td>\n",
+       "      <td>CA-2017-115427</td>\n",
+       "      <td>2017-12-30</td>\n",
+       "      <td>2018-01-03</td>\n",
+       "      <td>Standard Class</td>\n",
+       "      <td>Erica Bern</td>\n",
+       "      <td>Corporate</td>\n",
+       "      <td>United States</td>\n",
+       "      <td>Fairfield</td>\n",
+       "      <td>California</td>\n",
+       "      <td>...</td>\n",
+       "      <td>0.2</td>\n",
+       "      <td>6.4750</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0.329097</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5000 rows × 28 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "       Sno        Order ID Date of placing order Order Dispatch date  \\\n",
+       "0      740  CA-2014-112326            2014-01-04          2014-01-08   \n",
+       "1      741  CA-2014-112326            2014-01-04          2014-01-08   \n",
+       "2      742  CA-2014-112326            2014-01-04          2014-01-08   \n",
+       "3     1760  CA-2014-141817            2014-01-05          2014-01-12   \n",
+       "4      593  CA-2014-135405            2014-01-09          2014-01-13   \n",
+       "...    ...             ...                   ...                 ...   \n",
+       "4995   907  CA-2017-143259            2017-12-30          2018-01-03   \n",
+       "4996   908  CA-2017-143259            2017-12-30          2018-01-03   \n",
+       "4997   909  CA-2017-143259            2017-12-30          2018-01-03   \n",
+       "4998  1297  CA-2017-115427            2017-12-30          2018-01-03   \n",
+       "4999  1298  CA-2017-115427            2017-12-30          2018-01-03   \n",
+       "\n",
+       "      Logistics Type               Name      Segment        Country  \\\n",
+       "0     Standard Class      Phillina Ober  Home Office  United States   \n",
+       "1     Standard Class      Phillina Ober  Home Office  United States   \n",
+       "2     Standard Class      Phillina Ober  Home Office  United States   \n",
+       "3     Standard Class         Mick Brown     Consumer  United States   \n",
+       "4     Standard Class      Melanie Seite     Consumer  United States   \n",
+       "...              ...                ...          ...            ...   \n",
+       "4995  Standard Class  Patrick O'Donnell     Consumer  United States   \n",
+       "4996  Standard Class  Patrick O'Donnell     Consumer  United States   \n",
+       "4997  Standard Class  Patrick O'Donnell     Consumer  United States   \n",
+       "4998  Standard Class         Erica Bern    Corporate  United States   \n",
+       "4999  Standard Class         Erica Bern    Corporate  United States   \n",
+       "\n",
+       "               City         State  ...  Discount   Profit Unnamed: 20  \\\n",
+       "0        Naperville      Illinois  ...       0.2   4.2717           1   \n",
+       "1        Naperville      Illinois  ...       0.2 -64.7748           1   \n",
+       "2        Naperville      Illinois  ...       0.8  -5.4870           1   \n",
+       "3      Philadelphia  Pennsylvania  ...       0.2   4.8840           1   \n",
+       "4            Laredo         Texas  ...       0.2   1.1680           1   \n",
+       "...             ...           ...  ...       ...      ...         ...   \n",
+       "4995  New York City      New York  ...       0.2  12.1176          12   \n",
+       "4996  New York City      New York  ...       0.0   2.7279          12   \n",
+       "4997  New York City      New York  ...       0.2  19.7910          12   \n",
+       "4998      Fairfield    California  ...       0.2   4.5188          12   \n",
+       "4999      Fairfield    California  ...       0.2   6.4750          12   \n",
+       "\n",
+       "      log10000 Total Sales Month  Quarter  Unnamed: 25  Unnamed: 26  \\\n",
+       "0     0.267823   38127.933   Jan       Q1  39360.06045          NaN   \n",
+       "1     0.608936   21452.645   Feb      NaN          NaN          NaN   \n",
+       "2     0.137251  97859.6638   Mar      NaN          NaN          NaN   \n",
+       "3     0.322709  81724.5361   Apr       Q2  55751.25475          NaN   \n",
+       "4     0.242633  70289.3068   May      NaN          NaN          NaN   \n",
+       "...        ...         ...   ...      ...          ...          ...   \n",
+       "4995  0.627346         NaN   NaN      NaN          NaN          NaN   \n",
+       "4996  0.489677         NaN   NaN      NaN          NaN          NaN   \n",
+       "4997  0.430609         NaN   NaN      NaN          NaN          NaN   \n",
+       "4998  0.285785         NaN   NaN      NaN          NaN          NaN   \n",
+       "4999  0.329097         NaN   NaN      NaN          NaN          NaN   \n",
+       "\n",
+       "      Unnamed: 27  \n",
+       "0             NaN  \n",
+       "1             NaN  \n",
+       "2             NaN  \n",
+       "3             NaN  \n",
+       "4             NaN  \n",
+       "...           ...  \n",
+       "4995          NaN  \n",
+       "4996          NaN  \n",
+       "4997          NaN  \n",
+       "4998          NaN  \n",
+       "4999          NaN  \n",
+       "\n",
+       "[5000 rows x 28 columns]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "interpreter": {
+   "hash": "000b55af9c8c6e0b177305578cfd5e8b3858975f719edc1b51e24deccc4249ae"
+  },
+  "kernelspec": {
+   "display_name": "Python 3.9.7 64-bit ('minimal_ds': conda)",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.7"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/Statistics/README b/Statistics/README
new file mode 100644
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--- /dev/null
+++ b/Statistics/README
@@ -0,0 +1,11 @@
+I've taken a sales dataset from a reputed source and tried to fit distributions such as normal, beta and assess if its a good fit or not. 
+Two approaches were taken to arrive at the results:
+
+Approach 1: Calculate the theoretical and practical CDF's and compare it. Here, we considered two such CDF's i.e., Normal CDF and Beta CDF with suitable parameters.
+  -> Tools Used: Microsoft Excel
+  -> The Beta Fit and Normal Fit CDF graphs can be looked at their respective *.xlsx files.
+  -> Futhur explanations can be found in the "Calculations" pdf document.
+
+Approach 2: Estimate the Beta distribution parameters using "Method of Moments(MM)" and "Method of Maximum Likelihood(ML)" and compare the fit with its respective histogram.
+  -> Tools Used: Python and its packages such as 'scipy.stats','numpy','pandas','matplotlib'.
+ 
diff --git a/Statistics/Sales Dataset - Beta Fit.xlsx b/Statistics/Sales Dataset - Beta Fit.xlsx
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diff --git a/Statistics/Sales Dataset - Normal Fit.xlsx b/Statistics/Sales Dataset - Normal Fit.xlsx
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