08-the-central-limit-theorem.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random \n",
    "import math\n",
    "import scipy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import library_data_science as lds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Central Limit Theorem (CLT)\n",
    "\n",
    "Let us assume that for a certain population, we have selected a sufficiently large number of samples. Then, for each of them, we perform the same experiment, calculate the mean for each experiment, and record it. According to **the Central Limit Theorem (CLT)**, the resulting distribution of means **will always be normally distributed**.\n",
    "\n",
    "* This normal distribution will have a mean close to the mean of the population. $$Mean(\\text{means})\\approx Mean(\\text{population})$$\n",
    "\n",
    "* The variance will be close to the variance of population divided by the sample size. $$Variance(\\text{means})\\approx \\frac{Variance(\\text{population})}{\\text{sample.size}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, I will test the distribution of means from 10,000 trials, each consisting of rolling a die 100 times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dice = [1, 2, 3, 4, 5, 6]\n",
    "num_trials = 10000\n",
    "sample_size = 100\n",
    "\n",
    "means = []\n",
    "\n",
    "for trial in range(num_trials):\n",
    "    results = []\n",
    "\n",
    "    for attempt in range(sample_size):\n",
    "        results.append(random.choice(dice))\n",
    "    \n",
    "    trial_mean = lds.mean(results)\n",
    "    means.append(trial_mean)\n",
    "\n",
    "plt.hist(means, bins = 30)\n",
    "plt.axvline(lds.mean(means), label = f'Mean(means) = {np.round(lds.mean(means), 3)}', color = 'red')\n",
    "plt.xlabel('Mean from Sample')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a result, I obtained a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, I will try something more challenging. I will generate the distribution of means by testing 1,000 exponential distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_trials = 1000\n",
    "l = 0.9\n",
    "means = []\n",
    "\n",
    "for attempt in range(num_trials):\n",
    "    distribution = np.random.exponential(1 / l, size = 1000)\n",
    "    distribution_mean = lds.mean(distribution)\n",
    "    means.append(distribution_mean)\n",
    "\n",
    "X = np.linspace(0, 10, num = 1000)\n",
    "Y = [ lds.pdf_exponential(x, l) for x in X ]\n",
    "\n",
    "plt.plot(X, Y)\n",
    "[ plt.axvline(m, linestyle = '--', color = 'red') for m in means[::10]  ]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots depict the exponential distribution with $\\lambda = 0.9$, with dashed lines indicating the selected means for the generated distributions. It looks as if a single thick dashed line has formed because most of the means are concentrated in that area."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(means, bins = 15)\n",
    "plt.axvline(lds.mean(means), label = f'Mean(means) = {np.round(lds.mean(means), 3)}', color = 'red')\n",
    "plt.xlabel('Mean from Sample')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also as a result, I obtained a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final experiment will involve testing 1,000 Monte Carlo simulations to generate the value of $\\pi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_trials = 1000\n",
    "num_points = 100000\n",
    "\n",
    "results = []\n",
    "\n",
    "for trial in range(num_trials):\n",
    "    area = lds.area_monte_carlo(lambda x: (1 - x ** 2) ** 0.5, 0, 1, 0, 1, num_points = num_points)\n",
    "\n",
    "    results.append(4 * area)\n",
    "\n",
    "plt.hist(results, bins = 15)\n",
    "plt.axvline(lds.mean(results), label = f'Mean(means) = {np.round(lds.mean(results), 3)}', color = 'red')\n",
    "plt.xlabel('Mean from Sample')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After conducting all three tests, I have tangible confirmation of the Central Limit Theorem (CLT)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Standard Error\n",
    "\n",
    "**The Standard Error** is referred to as the Standard Deviation for the distribution of the means of the experiment. The smaller standard error, the better approximation we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means = []\n",
    "\n",
    "for attempt in range(1000):\n",
    "    dist = np.random.exponential(1 / 0.5, size = 1000)\n",
    "    means.append(lds.mean(dist))\n",
    "\n",
    "    if attempt == 100:\n",
    "        dist_mean = lds.mean(dist)\n",
    "        dist_std = lds.std(dist)\n",
    "        plt.hist(dist, bins = 15, weights = [ 1 / len(dist)] * len(dist), \\\n",
    "                 label = f'Mean(sample) = {np.round(dist_mean, 3)}, Std(sample) = {np.round(dist_std, 3)}')\n",
    "        plt.errorbar(x = [ dist_mean ], y = [ 0.4 ], xerr = [ dist_std ], fmt = 'o', capsize = 5, color = 'black')\n",
    "\n",
    "        X = np.linspace(0, 15, num = 1000)\n",
    "        Y = [ lds.pdf_exponential(x, 0.5) for x in X ]\n",
    "\n",
    "        plt.plot(X, Y, color = 'red', label = 'PDF')\n",
    "\n",
    "        plt.title('Histogram for additional sample generated in experiment')\n",
    "        plt.xlabel('Value')\n",
    "        plt.ylabel('Density')\n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "\n",
    "means_mean = lds.mean(means)\n",
    "means_std = lds.std(means)\n",
    "plt.hist(means, bins = 15, weights = [ 1 / len(means)] * len(means), \\\n",
    "            label = f'Mean(means) = {np.round(means_mean, 3)}, SE(means) = {np.round(means_std, 3)}')\n",
    "plt.errorbar(x = [ means_mean ], y = [ 0.125 ], xerr = [ means_std ], fmt = 'o', capsize = 5, color = 'black')\n",
    "\n",
    "plt.title('Histogram for the means')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I emphasize that in the case of a population or a sample, we refer to the **standard deviation** $Std(X)$, whereas when studying the distribution of means, we examine the **standard error** $SE(X)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Error with No Time-Consuming\n",
    "\n",
    "Calculating the standard error requires significant computational time or, in the case of live studies, a substantial number of experimental repetitions. However, there is an almost cost-free method for calculating the standard error using only the entire population or a sample.\n",
    "\n",
    "$$Standard\\_Error(\\text{sample}) = SE(\\text{sample}) = \\frac{Std_{s}(\\text{sample})}{\\sqrt{\\text{sample.size}}}$$\n",
    "\n",
    "When estimating the standard error from a sample, we must assume that the sample is **sufficiently representative** and **well-selected**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standard_error(sample: list):\n",
    "    return lds.std_s(sample) / (len(sample) ** 0.5)\n",
    "\n",
    "\n",
    "def se(sample: list):\n",
    "    return standard_error(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization of the Standard Error\n",
    "\n",
    "At this point, two common facts should be established.\n",
    "\n",
    "* More samples **will not change** the standard error.\n",
    "\n",
    "* Larger samples **will change** the standard error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify this, I will conduct two experiments involving the creation of a distribution of means for samples from an exponential distribution with $\\lambda = 0.2$. In the first experiment, I will increase the number of samples, while in the second, I will increase the sample size and compare the error bars for each of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment modifying the amount of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = [ 100, 200, 300, 400, 500, 600, 700, 800, 900 ]\n",
    "size = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = list(np.random.exponential(1 / l, size = 1000))\n",
    "\n",
    "means = []\n",
    "se_s = []\n",
    "\n",
    "for num_samples in samples:\n",
    "    dist_means = []\n",
    "\n",
    "    for attempt in range(num_samples):\n",
    "        sample = random.sample(population, size)\n",
    "        dist_means.append(lds.mean(sample))\n",
    "    \n",
    "    means.append(lds.mean(dist_means))\n",
    "    se_s.append(lds.std(dist_means))\n",
    "\n",
    "plt.errorbar(\n",
    "    x = samples,\n",
    "    y = means,\n",
    "    yerr = se_s,\n",
    "    fmt = 'o', capsize = 5, color = 'black'\n",
    ")\n",
    "\n",
    "plt.title('Experiment modifying the amount of samples')\n",
    "plt.xlabel('Amount of samples')\n",
    "plt.ylabel('Mean')\n",
    "plt.axhline(lds.mean(means), linestyle = '--', color = 'red', label = 'Mean of the Means')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The experiment proves that the number of trials doesn't matter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment modifying the sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = 100\n",
    "sizes = [ 100, 200, 300, 400, 500, 600, 700, 800, 900 ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = list(np.random.exponential(1 / l, size = 1000))\n",
    "\n",
    "means = []\n",
    "se_s = []\n",
    "\n",
    "for size in sizes:\n",
    "    dist_means = []\n",
    "\n",
    "    for attempt in range(num_samples):\n",
    "        sample = random.sample(population, size)\n",
    "        dist_means.append(lds.mean(sample))\n",
    "    \n",
    "    means.append(lds.mean(dist_means))\n",
    "    se_s.append(lds.std(dist_means))\n",
    "\n",
    "plt.errorbar(\n",
    "    x = sizes,\n",
    "    y = means,\n",
    "    yerr = se_s,\n",
    "    fmt = 'o', capsize = 5, color = 'black'\n",
    ")\n",
    "\n",
    "plt.title('Experiment modifying the amount of samples')\n",
    "plt.xlabel('Size of each sample')\n",
    "plt.ylabel('Mean')\n",
    "plt.axhline(lds.mean(means), linestyle = '--', color = 'red', label = 'Mean of the Means')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The experiment clearly proves that it is the sample size that matters, not the number of trials."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}