{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats\n",
    "from scipy.stats import norm, expon\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "DataWhr2024 = pd.read_csv(\"DataWhr2024.csv\")\n",
    "UnM49 = pd.read_csv(\"UnM49.csv\", sep=';')\n",
    "\n",
    "UnM49 = UnM49[['Country or Area', 'Sub-region Name', 'Region Name']]\n",
    "UnM49 = UnM49.rename({'Country or Area':'Country name', 'Sub-region Name':'Subregion', 'Region Name':'Continent'}, axis=1)\n",
    "\n",
    "DataWhr2024.loc[DataWhr2024[\"Country name\"].str.startswith(\"Hong\"), \"Country name\"] = \"Hong Kong\"\n",
    "DataWhr2024.loc[DataWhr2024[\"Country name\"].str.startswith(\"Somaliland\"), \"Country name\"] = \"Somaliland\"\n",
    "DataWhr2024.loc[DataWhr2024[\"Country name\"].str.startswith(\"Taiwan\"), \"Country name\"] = \"Taiwan\"\n",
    "\n",
    "UnM49.loc[97, \"Country name\"] = \"Bolivia\"\n",
    "UnM49.loc[33, \"Country name\"] = \"Congo (Brazzaville)\"\n",
    "UnM49.loc[34, \"Country name\"] = \"Congo (Kinshasa)\"\n",
    "UnM49.loc[124, \"Country name\"] = \"Hong Kong\"\n",
    "UnM49.loc[125, \"Country name\"] = \"Macao\"\n",
    "UnM49.loc[126, \"Country name\"] = \"North Korea\"\n",
    "UnM49.loc[145, \"Country name\"] = \"Iran\"\n",
    "UnM49.loc[46, \"Country name\"] = \"Ivory Coast\"\n",
    "UnM49.loc[133, \"Country name\"] = \"Laos\"\n",
    "UnM49.loc[129, \"Country name\"] = \"South Korea\"\n",
    "UnM49.loc[173, \"Country name\"] = \"Moldova\"\n",
    "UnM49.loc[217, \"Country name\"] = \"Netherlands\"\n",
    "UnM49.loc[175, \"Country name\"] = \"Russia\"\n",
    "UnM49.loc[164, \"Country name\"] = \"Syria\"\n",
    "UnM49.loc[26, \"Country name\"] = \"Tanzania\"\n",
    "UnM49.loc[116, \"Country name\"] = \"United States\"\n",
    "UnM49.loc[193, \"Country name\"] = \"United Kingdom\"\n",
    "UnM49.loc[111, \"Country name\"] = \"Venezuela\"\n",
    "UnM49.loc[140, \"Country name\"] = \"Vietnam\"\n",
    "\n",
    "_ = pd.DataFrame(\n",
    "    {\n",
    "        \"Country name\": [\"Kosovo\", \"Somaliland\", \"Taiwan\"],\n",
    "        \"Subregion\": [\"Southern Europe\", \"Sub-Saharan Africa\", \"Eastern Asia\"],\n",
    "        \"Continent\": [\"Europe\", \"Africa\", \"Asia\"],\n",
    "    }\n",
    ")\n",
    "\n",
    "UnM49 = pd.concat([UnM49, _], axis=0)\n",
    "UnM49 = UnM49.reset_index(drop=True)\n",
    "\n",
    "# Data\n",
    "Dat = pd.merge(DataWhr2024, UnM49)\n",
    "\n",
    "# Data of 2023\n",
    "Dat2023 = Dat[Dat['year'] == 2023]\n",
    "Dat2023 = Dat2023.reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) P(20 < X ≤ 40): 0.625475\n",
      "(b) P(X > 60): 0.000179\n",
      "(c) P(X ≤ 30): 0.097141\n",
      "(d) P(X = 35): 0.057498\n"
     ]
    }
   ],
   "source": [
    "# Define parameters for the normal distribution\n",
    "# Assuming p (breast cancer rate) is known; set an example p = 0.0005 (0.05%)\n",
    "p = 38/100000\n",
    "n = 100000\n",
    "mu = n * p  # Mean\n",
    "sigma = (n * p * (1 - p))**0.5  # Standard deviation\n",
    "\n",
    "# Define the normal distribution\n",
    "normal_dist = norm(loc=mu, scale=sigma)\n",
    "\n",
    "# (a) P(20 < X ≤ 40)\n",
    "prob_a = normal_dist.cdf(40) - normal_dist.cdf(20)\n",
    "\n",
    "# (b) P(X > 60)\n",
    "prob_b = 1 - normal_dist.cdf(60)\n",
    "\n",
    "# (c) P(X ≤ 30)\n",
    "prob_c = normal_dist.cdf(30)\n",
    "\n",
    "# (d) P(X = 35)\n",
    "# For continuous distributions, the probability at an exact point is 0, \n",
    "# so use the probability density function (PDF) to approximate it.\n",
    "prob_d = normal_dist.pdf(35)\n",
    "\n",
    "# Print results with 6 decimal places\n",
    "print(f\"(a) P(20 < X ≤ 40): {prob_a:.6f}\")\n",
    "print(f\"(b) P(X > 60): {prob_b:.6f}\")\n",
    "print(f\"(c) P(X ≤ 30): {prob_c:.6f}\")\n",
    "print(f\"(d) P(X = 35): {prob_d:.6f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) Probability Life Ladder > 5 (Normal): 0.707072\n",
      "(a) Probability Life Ladder > 5 (Empirical): 0.702899\n",
      "(b) Probability 4 ≤ Life Ladder ≤ 7 (Normal): 0.809476\n",
      "(b) Probability 4 ≤ Life Ladder ≤ 7 (Empirical): 0.833333\n"
     ]
    }
   ],
   "source": [
    "Dat1 = Dat2023['Life Ladder']\n",
    "\n",
    "meanLL = Dat1.mean()\n",
    "stdLL = Dat1.std()\n",
    "\n",
    "normal_dist = norm(loc=meanLL, scale=stdLL)\n",
    "\n",
    "# Calculate mean and standard deviation of Life Ladder\n",
    "meanLL = Dat1.mean()\n",
    "stdLL = Dat1.std()\n",
    "\n",
    "# Define the normal distribution with calculated parameters\n",
    "normal_dist = norm(loc=meanLL, scale=stdLL)\n",
    "\n",
    "# (a) Probability that Life Ladder > 5\n",
    "prob_normal_a = 1 - normal_dist.cdf(5)  # Using the normal distribution\n",
    "prob_empirical_a = (Dat1 > 5).mean()  # Empirical probability from dataset\n",
    "\n",
    "# (b) Probability that Life Ladder is between 4 and 7\n",
    "prob_normal_b = normal_dist.cdf(7) - normal_dist.cdf(4)  # Using the normal distribution\n",
    "prob_empirical_b = ((Dat1 >= 4) & (Dat1 <= 7)).mean()  # Empirical probability from dataset\n",
    "\n",
    "# (c) Histogram and density plot\n",
    "plt.hist(Dat1, bins=20, density=True, alpha=0.6, color='skyblue', label='Histogram')\n",
    "x_values = np.linspace(min(Dat1), max(Dat1), 1000)\n",
    "plt.plot(x_values, normal_dist.pdf(x_values), color='red', label='Normal Density')\n",
    "plt.xlabel('Life Ladder')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Histogram and Normal Distribution Density')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Print results\n",
    "print(f\"(a) Probability Life Ladder > 5 (Normal): {prob_normal_a:.6f}\")\n",
    "print(f\"(a) Probability Life Ladder > 5 (Empirical): {prob_empirical_a:.6f}\")\n",
    "print(f\"(b) Probability 4 ≤ Life Ladder ≤ 7 (Normal): {prob_normal_b:.6f}\")\n",
    "print(f\"(b) Probability 4 ≤ Life Ladder ≤ 7 (Empirical): {prob_empirical_b:.6f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group 1 (stain=1) - σ: 127.08, λ: 0.01\n",
      "Group 2 (stain=2) - σ: 83.72, λ: 0.01\n",
      "Probability that Group 1 survives more than 10 years: 0.3889\n",
      "Probability that Group 2 survives more than 10 years: 0.2385\n",
      "Probability that Group 1 dies within 3 years: 0.2467\n",
      "Probability that Group 2 dies within 3 years: 0.3495\n"
     ]
    }
   ],
   "source": [
    "# Load the dataset (replace 'PrognosisWomenBreastCancer.csv' with the actual file path)\n",
    "DatBreastCancer = pd.read_csv(\"PrognosisWomenBreastCancer.csv\")\n",
    "\n",
    "# Check the structure of the dataset to find relevant columns\n",
    "# Assuming 'time_of_death' is the column representing time of death in months and 'stain' is the group column\n",
    "#print(DatBreastCancer.head())\n",
    "\n",
    "# Separate the data into two groups based on 'stain' (1 or 2)\n",
    "group_1 = DatBreastCancer[DatBreastCancer['stain'] == 1]['time']\n",
    "group_2 = DatBreastCancer[DatBreastCancer['stain'] == 2]['time']\n",
    "\n",
    "# Calculate the mean (σ) for each group, which corresponds to the scale parameter of the exponential distribution\n",
    "sigma_1 = group_1.mean()\n",
    "sigma_2 = group_2.mean()\n",
    "\n",
    "# Calculate the rate parameter λ (inverse of σ) for each group\n",
    "lambda_1 = 1 / sigma_1\n",
    "lambda_2 = 1 / sigma_2\n",
    "\n",
    "# (b) Calculate the probability that each survives more than 10 years (120 months)\n",
    "# P(X > 120) = e^(-120 / σ)\n",
    "survival_1 = np.exp(-120 / sigma_1)\n",
    "survival_2 = np.exp(-120 / sigma_2)\n",
    "\n",
    "# (c) Calculate the probability that each dies within the next 3 years (36 months)\n",
    "# P(X <= 36) = 1 - e^(-36 / σ)\n",
    "death_1 = 1 - np.exp(-36 / sigma_1)\n",
    "death_2 = 1 - np.exp(-36 / sigma_2)\n",
    "\n",
    "# Print the results\n",
    "print(f\"Group 1 (stain=1) - σ: {sigma_1:.2f}, λ: {lambda_1:.2f}\")\n",
    "print(f\"Group 2 (stain=2) - σ: {sigma_2:.2f}, λ: {lambda_2:.2f}\")\n",
    "print(f\"Probability that Group 1 survives more than 10 years: {survival_1:.4f}\")\n",
    "print(f\"Probability that Group 2 survives more than 10 years: {survival_2:.4f}\")\n",
    "print(f\"Probability that Group 1 dies within 3 years: {death_1:.4f}\")\n",
    "print(f\"Probability that Group 2 dies within 3 years: {death_2:.4f}\")\n"
   ]
  }
 ],
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