CLT.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Manish-k723/100-days-of-ML/blob/main/CLT.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "B4Qg4JoFfH7X"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n = 10  # number of trials\n",
        "p = 0.1  # probability of success\n",
        "size = 1000  # number of samples to generate\n",
        "\n",
        "binomial_dist = np.random.binomial(n, p, size)\n",
        "\n",
        "plt.hist(binomial_dist,density=True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "aYU6WgqPfhFp",
        "outputId": "c6051e24-c97f-44e4-d13a-63a0eee8d504"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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L5w5sBB6qqr8Y7Uir9jPAR3onpGeAnxjmg4/V2xYlSSsbt0sukqQVGHRJaoRBl6RGGHRJaoRBl6RGGHRJaoRBl6RG/A8Ex6ufm0XAFAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Set the parameters\n",
        "num_samples = 10000\n",
        "sample_size = 300\n",
        "distribution_range = (0, 1)\n",
        "\n",
        "# Generate samples from a uniform distribution\n",
        "samples = np.random.uniform(distribution_range[0], distribution_range[1], (num_samples, sample_size))\n",
        "\n",
        "# Calculate the sample means\n",
        "sample_means = np.mean(samples, axis=1)\n",
        "\n",
        "# Plot the histogram of the sample means\n",
        "plt.hist(sample_means, bins=30, density=True, edgecolor='black')\n",
        "plt.title('Histogram of Sample Means')\n",
        "plt.xlabel('Sample Mean')\n",
        "plt.ylabel('Density')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "WlQgIHA9iJPT",
        "outputId": "c313b30a-4621-4d75-e1a9-8b7d53b79f7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Set the parameters\n",
        "num_samples = 1000\n",
        "sample_size = 50\n",
        "lambda_param = 2\n",
        "\n",
        "# Generate samples from an exponential distribution\n",
        "samples = np.random.exponential(scale=1/lambda_param, size=(num_samples, sample_size))\n",
        "\n",
        "# Calculate the sample means\n",
        "sample_means = np.mean(samples, axis=1)\n",
        "\n",
        "# Plot the histogram of the sample means\n",
        "plt.hist(sample_means, bins=30, density=True, edgecolor='black')\n",
        "plt.title('Histogram of Sample Means (Exponential Distribution)')\n",
        "plt.xlabel('Sample Mean')\n",
        "plt.ylabel('Density')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "jBdPqh9goUtg",
        "outputId": "87f5bdbb-37f7-4909-b9f5-6ae6f6f6575e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Set the parameters\n",
        "num_samples = 1000\n",
        "sample_size = 50\n",
        "\n",
        "# Poisson distribution parameters\n",
        "poisson_lambda = 5\n",
        "\n",
        "# Gamma distribution parameters\n",
        "gamma_shape = 2\n",
        "gamma_scale = 1\n",
        "\n",
        "# Binomial distribution parameters\n",
        "binomial_n = 10\n",
        "binomial_p = 0.5\n",
        "\n",
        "# Generate samples from the distributions\n",
        "poisson_samples = np.random.poisson(lam=poisson_lambda, size=(num_samples, sample_size))\n",
        "gamma_samples = np.random.gamma(shape=gamma_shape, scale=gamma_scale, size=(num_samples, sample_size))\n",
        "binomial_samples = np.random.binomial(n=binomial_n, p=binomial_p, size=(num_samples, sample_size))\n",
        "\n",
        "# Calculate the sample means\n",
        "poisson_means = np.mean(poisson_samples, axis=1)\n",
        "gamma_means = np.mean(gamma_samples, axis=1)\n",
        "binomial_means = np.mean(binomial_samples, axis=1)\n",
        "\n",
        "# Plot the histograms of the sample means\n",
        "fig, axs = plt.subplots(3, 1, figsize=(8, 12))\n",
        "\n",
        "# Poisson distribution\n",
        "axs[0].hist(poisson_means, bins=30, density=True, edgecolor='black')\n",
        "axs[0].set_title('Histogram of Sample Means (Poisson Distribution)')\n",
        "axs[0].set_xlabel('Sample Mean')\n",
        "axs[0].set_ylabel('Density')\n",
        "\n",
        "# Gamma distribution\n",
        "axs[1].hist(gamma_means, bins=30, density=True, edgecolor='black')\n",
        "axs[1].set_title('Histogram of Sample Means (Gamma Distribution)')\n",
        "axs[1].set_xlabel('Sample Mean')\n",
        "axs[1].set_ylabel('Density')\n",
        "\n",
        "# Binomial distribution\n",
        "axs[2].hist(binomial_means, bins=30, density=True, edgecolor='black')\n",
        "axs[2].set_title('Histogram of Sample Means (Binomial Distribution)')\n",
        "axs[2].set_xlabel('Sample Mean')\n",
        "axs[2].set_ylabel('Density')\n",
        "\n",
        "# Adjust the layout and show the plot\n",
        "fig.tight_layout()\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 873
        },
        "id": "kQNpAKeEooeM",
        "outputId": "72b46397-adb8-4176-bea0-ceca45c4dea2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x864 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# CLT Demo Gamma Distribution"
      ],
      "metadata": {
        "id": "AT6yMOCt7p5F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Set the parameters\n",
        "num_samples = 10000\n",
        "sample_size = 50\n",
        "\n",
        "# Gamma distribution parameters\n",
        "gamma_shape = 2\n",
        "gamma_scale = 1\n",
        "\n",
        "# Calculate the theoretical mean and variance\n",
        "theoretical_mean = gamma_shape * gamma_scale\n",
        "theoretical_variance = (gamma_shape * gamma_scale ** 2)\n",
        "\n",
        "# Generate samples from the Gamma distribution\n",
        "samples = np.random.gamma(shape=gamma_shape, scale=gamma_scale, size=(num_samples, sample_size))\n",
        "\n",
        "# Calculate the sample means\n",
        "sample_means = np.mean(samples, axis=1)\n",
        "\n",
        "# Calculate the empirical mean and variance of the sample means\n",
        "empirical_mean = np.mean(sample_means)\n",
        "empirical_variance = np.var(sample_means)\n",
        "\n",
        "# Compare the theoretical and empirical values\n",
        "print(f\"Theoretical mean: {theoretical_mean:.4f}\")\n",
        "print(f\"Empirical mean: {empirical_mean:.4f}\")\n",
        "print(f\"\\n\")\n",
        "print(f\"Theoretical variance: {theoretical_variance:.4f}\")\n",
        "print(f\"Empirical variance: {empirical_variance:.4f}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wczh1MGWrKu-",
        "outputId": "bb0c4e29-80f8-4846-ae7a-cbd46afb1b82"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Theoretical mean: 2.0000\n",
            "Empirical mean: 2.0009\n",
            "\n",
            "\n",
            "Theoretical variance: 2.0000\n",
            "Empirical variance: 0.0395\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "2.0000/50"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mng5NEYU4M5M",
        "outputId": "33703bb3-7ed9-47c1-930f-f9120e690282"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.04"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# CLT Demo Log Normal Distribution"
      ],
      "metadata": {
        "id": "1dMCwb8Os6jT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Set the parameters\n",
        "num_samples = 10000\n",
        "sample_size = 50\n",
        "\n",
        "# Log-Normal distribution parameters\n",
        "mu = 0.5\n",
        "sigma = 0.7\n",
        "\n",
        "# Calculate the theoretical mean and variance\n",
        "theoretical_mean = np.exp(mu + (sigma ** 2) / 2)\n",
        "theoretical_variance = (np.exp(sigma ** 2) - 1) * np.exp(2 * mu + sigma ** 2)\n",
        "\n",
        "# Generate samples from the Log-Normal distribution\n",
        "samples = np.random.lognormal(mean=mu, sigma=sigma, size=(num_samples, sample_size))\n",
        "\n",
        "# Calculate the sample means\n",
        "sample_means = np.mean(samples, axis=1)\n",
        "\n",
        "# Calculate the empirical mean and variance of the sample means\n",
        "empirical_mean = np.mean(sample_means)\n",
        "empirical_variance = np.var(sample_means)\n",
        "\n",
        "# Compare the theoretical and empirical values\n",
        "print(f\"Theoretical mean: {theoretical_mean:.4f}\")\n",
        "print(f\"Empirical mean: {empirical_mean:.4f}\")\n",
        "print(f\"\\n\")\n",
        "print(f\"Theoretical variance: {theoretical_variance:.4f}\")\n",
        "print(f\"Empirical variance: {empirical_variance:.4f}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ytt83w9ZtOtj",
        "outputId": "5f41fad2-812e-45c4-b376-d7e4b1f7bde1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Theoretical mean: 2.1064\n",
            "Empirical mean: 2.1028\n",
            "\n",
            "\n",
            "Theoretical variance: 2.8056\n",
            "Empirical variance: 0.0560\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "EJyIyvBrtdBc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# CLT Case Study"
      ],
      "metadata": {
        "id": "fAJUPbqD7Vyo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Set the parameters\n",
        "population_size = 100000\n",
        "sample_size = 50\n",
        "num_samples = 100\n",
        "\n",
        "# Generate a random representative sample of salaries (in thousands)\n",
        "# You should replace this with actual collected salary data\n",
        "np.random.seed(42)  # Setting a seed for reproducibility\n",
        "population_salaries = np.random.lognormal(mean=4.5, sigma=0.8, size=population_size)\n",
        "\n",
        "# Generate multiple samples and calculate the sample means and standard deviations\n",
        "sample_means = []\n",
        "sample_std_devs = []\n",
        "\n",
        "for _ in range(num_samples):\n",
        "  sample_salaries = np.random.choice(population_salaries, size=sample_size)\n",
        "  sample_means.append(np.mean(sample_salaries))\n",
        "  sample_std_devs.append(np.std(sample_salaries))\n",
        "\n",
        "# Calculate the average of the sample means and the standard error\n",
        "average_sample_means = np.mean(sample_means)\n",
        "standard_error = np.std(sample_means) / np.sqrt(num_samples)\n",
        "\n",
        "# Calculate the 95% confidence interval\n",
        "margin_of_error = 1.96 * standard_error\n",
        "lower_limit = average_sample_means - margin_of_error\n",
        "upper_limit = average_sample_means + margin_of_error\n",
        "\n",
        "# Report the results\n",
        "print(f\"Estimated average salary (in thousands): {average_sample_means:.2f}\")\n",
        "print(f\"95% confidence interval (in thousands): ({lower_limit:.2f}, {upper_limit:.2f})\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uYZgnbUKvqYO",
        "outputId": "c7445d72-948c-4464-8e34-924f1c398ae8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimated average salary (in thousands): 124.74\n",
            "95% confidence interval (in thousands): (121.23, 128.26)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "UPfxXKaD7TFf"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}