ArtStudies/L3/Statistiques/TP1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "10b8aa2c-cf98-4170-966c-a1f5e6e7f55a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "52e1d61e-cde8-47ec-94d8-285dab47089e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f834444ca30>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = 1\n",
    "nb_repl = 100000\n",
    "sample = np.random.exponential(lam, nb_repl)\n",
    "intervalle = np.linspace(0, 5, 100)\n",
    "plt.hist(sample, bins=intervalle, density=True, label=\"Echantillon\")\n",
    "\n",
    "densite = stats.expon().pdf\n",
    "plt.plot(intervalle, densite(intervalle), label=\"Fonction densité\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "168e2038-b080-4a28-b56a-61d6cd26c4d3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f833c22b7c0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np_repl = 10000\n",
    "sampleX, sampleY = 2 * np.random.rand(np_repl) - 1, 2 * np.random.rand(np_repl) - 1\n",
    "\n",
    "intervalle = np.linspace(-2, 2, 100)\n",
    "plt.hist(sampleX + sampleY, bins=intervalle, density=True, label=\"Echantillon\")\n",
    "\n",
    "densite = stats.uniform(-1, 2).pdf\n",
    "plt.plot(intervalle, densite(intervalle), label=\"Fonction densité\")\n",
    "\n",
    "plt.plot(intervalle, 1 / 4 * np.maximum(2 - np.abs(intervalle), 0), label=\"Fonction\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9db2df29-5793-4275-be83-20e7a88ab194",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f833c3d9060>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = 1\n",
    "nb_repl = 10000\n",
    "sampleX, sampleY, sampleZ = (\n",
    "    np.random.exponential(lam, nb_repl),\n",
    "    np.random.exponential(lam, nb_repl),\n",
    "    np.random.exponential(lam, nb_repl),\n",
    ")\n",
    "intervalle = np.linspace(-5, 5, 100)\n",
    "plt.hist(\n",
    "    sampleX - sampleY / 2,\n",
    "    bins=intervalle,\n",
    "    density=True,\n",
    "    alpha=0.7,\n",
    "    label=\"Echantillon de X - Y/2\",\n",
    ")\n",
    "plt.hist(\n",
    "    sampleZ / 2, bins=intervalle, density=True, alpha=0.7, label=\"Echantillon de Z\"\n",
    ")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "14d34eed-3ca6-48c6-a004-97436d750d73",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 1 / 2\n",
    "nb_repl = 1000\n",
    "\n",
    "plt.figure(figsize=(18, 5))\n",
    "for i, k in enumerate([10, 100, 1000]):\n",
    "    plt.subplot(1, 3, i + 1)\n",
    "    sample = np.random.binomial(k, p, nb_repl)\n",
    "    intervalle = np.linspace(np.min(sample), np.max(sample), 100)\n",
    "    plt.hist(\n",
    "        sample, bins=intervalle, density=True, label=f\"Echantillon de X pour n={k}\"\n",
    "    )\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0c6898fa-3cb8-4bec-9153-73ce08a95809",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def sample_uniforme(N):\n",
    "    return 2 * np.random.rand(N) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "63bd382b-8c4e-4eaa-93b3-20ae561811c9",
   "metadata": {
    "tags": []
   },
   "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": [
    "nb_repl = 100_000\n",
    "nb_lgn = 1000\n",
    "liste_Sn = []\n",
    "\n",
    "for _ in range(nb_lgn):\n",
    "    liste_Sn.append(np.mean(sample_uniforme(nb_repl)))\n",
    "\n",
    "nb_bins = 100\n",
    "intervalles = np.linspace(np.min(liste_Sn), np.max(liste_Sn), nb_bins)\n",
    "plt.hist(liste_Sn, density=True, bins=intervalles)\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "nb_bins = 100\n",
    "intervalles = np.linspace(-1, 1, nb_bins)\n",
    "plt.hist(liste_Sn, density=True, bins=intervalles)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41ddaed5-d548-43f5-97ab-148f653e99da",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nb_repl = 100_000\n",
    "nb_lgn = 1000\n",
    "liste_Sn = []\n",
    "\n",
    "for _ in range(nb_lgn):\n",
    "    liste_Sn.append(\n",
    "        np.mean(np.sqrt(3 * nb_repl) * np.tan(np.pi / 2 * sample_uniforme(nb_repl)))\n",
    "    )\n",
    "\n",
    "# nb_bins = 100\n",
    "# intervalles = np.linspace(np.min(liste_Sn), np.max(liste_Sn), nb_bins)\n",
    "# plt.hist(liste_Sn, density=True, bins=intervalles)\n",
    "# plt.show()\n",
    "\n",
    "plt.figure()\n",
    "densite = stats.norm(scale=1).pdf\n",
    "nb_bins = 100\n",
    "intervalles = np.linspace(-1000, 1000, nb_bins)\n",
    "plt.hist(liste_Sn, density=True, bins=intervalles)\n",
    "plt.plot(intervalle, densite(intervalle))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0733430b-464e-486b-a66e-e89c7abc37b9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}