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    "# MDI 720 : Statistiques\n",
    "## IntroIC\n",
    "### *Joseph Salmon*\n",
    "\n",
    "This notebook reproduces the pictures for the course \"IntroStatics\"\n",
    "\n",
    "REM:\n",
    "  - you need TeX install on your machine (otherwise errors could appends)\n",
    "  - you need plot_species_kde.py in the same directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import packages\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt  # for plots\n",
    "from matplotlib import rc\n",
    "import seaborn as sns\n",
    "from os import mkdir, path\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from statsmodels.nonparametric.kde import KDEUnivariate\n",
    "from scipy.stats import norm\n",
    "sns.set_style(\"white\")\n",
    "sns.set_palette(\"Blues\")\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "saving = True\n",
    "dirname = \"../prebuiltimages/\"\n",
    "imageformat = '.pdf'\n",
    "\n",
    "if not path.exists(dirname):\n",
    "    mkdir(dirname)\n",
    "\n",
    "def my_saving_display(fig, dirname, filename, imageformat):\n",
    "    \"\"\"\"Saving with personal function.\"\"\"\n",
    "    filename = filename.replace('.', 'pt')  # remove \".\" to avoid floats issues\n",
    "    if saving is True:\n",
    "        dirname + filename + imageformat\n",
    "        image_name = dirname + filename + imageformat\n",
    "        fig.savefig(image_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_repetition = 500\n",
    "tab_n_samples =  [5, 20, 50, 500]\n",
    "np.random.seed(seed=44)\n",
    "fig = plt.figure()\n",
    "for i, n_samples in enumerate(tab_n_samples):\n",
    "    X = np.random.randn(n_samples, n_repetition)\n",
    "    vect_1n = np.arange(1,n_samples + 1)    \n",
    "    kde = KDEUnivariate(np.sort(np.mean(X,0) * np.sqrt(n_samples)))\n",
    "    kde.fit(bw=0.25, kernel='gau')\n",
    "    x_grid = np.linspace(-3, 3, 100)\n",
    "    pdf_est = kde.evaluate(x_grid)\n",
    "    plt.plot(x_grid, pdf_est,label=str(n_samples))\n",
    "\n",
    "plt.plot(x_grid, norm.pdf(x_grid), c='k', linewidth=2,label=\"asymptotic\")\n",
    "plt.legend()\n",
    "plt.title('TCL: convergence of $\\\\bar{y}_n$ density w.r.t the number of samples')\n",
    "plt.show()\n",
    "\n",
    "my_saving_display(fig, dirname, \"TCL_illustration\", imageformat)"
   ]
  }
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