Commit f735ec7a authored by vincentvigon's avatar vincentvigon
Browse files

passage a gitlab

parent 23e577d5
This source diff could not be displayed because it is too large. You can view the blob instead.
This source diff could not be displayed because it is too large. You can view the blob instead.
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Plus de lois avec scipy"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"np.set_printoptions(precision=2,suppress=True)\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\"\"\"Voici un autre import qu'il faut connaître :\n",
"scipy= sci-entific py-thon \"\"\"\n",
"import scipy.stats as stats\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"4 mots clefs à retenir (qui permettent aussi d'améliorer son anglais scientifique) :\n",
"\n",
"* pdf -> Probability density function. -> densité (prend des réels en argument)\n",
"* pmf -> Probability mass function -> densité discrète (prend des entiers en argument)\n",
"\n",
"* cdf -> Cumulative density function. -> fonction de répartition\n",
"* ppf -> Percent point function (inverse of cdf ) -> fonction quantile (ou percentile)\n",
"\n",
"* rvs -> Random variates. -> simulation d'un échantillon de va ayant la loi donnée\n",
"\n",
"\n",
"A ce point du TP, vous vous dites qu'il y a vraiment trop de choses à retenir. Mais nous\n",
"allons les pratiquez très souvent : cela rentrera tout seul."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Densité, fonction de réparition, quantiles"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### une loi continue"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/vigon/Library/Python/3.6/lib/python/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
" warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 720x360 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"simus=stats.norm.rvs(loc=0, scale=1, size=1000)\n",
"\"\"\"\n",
"c'est tout à fait identique à :\n",
"simus=np.random.normal(loc=0,scale=1,size=1000)\n",
"\n",
"cependant scipy.stats contient encore plus de loi que numpy.random.\n",
"Par exemple la loi t de student utile pour les stats.\n",
"\"\"\"\n",
"plt.figure(figsize=(10,5))\n",
"\n",
"\n",
"x=np.linspace(-3,3,100)\n",
"pdf=stats.norm.pdf(x, loc=0, scale=1)\n",
"cdf=stats.norm.cdf(x, loc=0, scale=1)\n",
"ppf=stats.norm.ppf(x, loc=0, scale=1)\n",
"\n",
"plt.subplot(1,2,1)\n",
"plt.hist(simus,20,normed=True,label=\"simus\",edgecolor=\"k\")\n",
"plt.plot(x,pdf,label=\"pdf\")\n",
"plt.plot(x,cdf,label=\"cdf\")\n",
"plt.legend()\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.plot(x, cdf,label=\"cdf\")\n",
"plt.plot(x, ppf,label=\"ppf\")\n",
"plt.plot(x, x,label=\"y=x\")\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le tracé de la ppf ci-dessus n'est pas très joli, on a l'impression qu'il est incomplet.\n",
"Changez cela. \n",
"\n",
"Aide: n'oubliez pas qu'une courbe, c'est des points qu'on relie entre eux, et que ces points, c'est vous qui les spécifiez. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### une loi discrète"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/vigon/Library/Python/3.6/lib/python/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
" warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n=10\n",
"p=0.5\n",
"simus=stats.binom.rvs(n, p, size=1000)\n",
"\n",
"\n",
"x=np.arange(0,n+1)\n",
"bins=np.arange(0,n+2)-0.5\n",
"\"\"\" attention, la densité discréte en scipy c'est pmf et pas pdf \"\"\"\n",
"pdf=stats.binom.pmf(x, n, p)\n",
"cdf=stats.binom.cdf(x, n, p)\n",
"\n",
"\n",
"plt.hist(simus, bins, normed=True, label=\"simus\",edgecolor=\"k\")\n",
"plt.plot(x, pdf,'o' , label=\"pdf\")\n",
"plt.plot(x, cdf,'o', label=\"cdf\")\n",
"plt.title(\"loi binomiale\")\n",
"plt.legend();\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 936x360 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\" variante. On trace la fonction de répartition en escalier. \n",
"On rajoute des lignes verticales pour vous aidez dans l'exo suivant\"\"\"\n",
"plt.figure(figsize=(13,5))\n",
"\n",
"plt.subplot(1,2,1)\n",
"\"\"\" lignes verticales. \"\"\"\n",
"for xc in x:plt.axvline(x=xc, color='0.9') #0.9 => un gris très clair (0=noir,1=blanc)\n",
"plt.plot(x, cdf,drawstyle='steps-post')\n",
"plt.xticks(x)\n",
"\n",
"\n",
"plt.subplot(1,2,2)\n",
"for xc in x:plt.axvline(x=xc, color='0.9')\n",
"plt.plot(x, cdf,drawstyle='steps-pre')\n",
"plt.xticks(x);\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"***Exo:*** laquelle de ces deux représentations correpond à la fonction de répartition, à savoir: \n",
"\t$x \\to P[ X\\leq x]$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"***Conseil:*** lisez bien les messages d'erreur. Par exemple si vous écrivez :\n",
" `plt.plot(x,y,drawstyle='steps-after',color=\"red\")`\n",
"cela provoque un message d'erreur :\n",
"\n",
" ValueError: Unrecognized drawstyle steps-pre default steps-post steps-mid steps\n",
"\n",
"Ce message nous indique que l'on c'est tromper de mot clef, et nous propose les mot clefs valides. \n",
"D'après vous, quand on écrit `drawstyle=default`, comment les points sont reliés ?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conseil python: les arguments facultatifs\n",
"\n",
"Considérons un appel d'une fonction de scipy :"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"stats.norm.rvs(loc=-1,scale=3,size=100);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Tous les arguments sont facultatifs. Les valeurs par défaut sont logiquement `loc=0,scale=1,size=1`\n",
"On peut écrire par exemple \n",
"\n",
" simus=stat.norm.rvs(size=1000)\n",
"\n",
"pour\n",
"\n",
" simus=stat.norm.rvs(loc=0,scale=1,size=1000)\n",
"\n",
"\n",
"Mais attention : si on ne précise pas le nom des arguments, ils sont pris dans l'ordre `1:loc 2:scale 3:size`\n",
"Par exemple, si je veux tirer 1000 gaussienne et que j'écris\n",
"\n",
" simus=stat.norm.rvs(1000)\n",
"\n",
"mon programme bug car cela correspond à \n",
"\n",
" simus=stat.norm.rvs(loc=1000)\n",
"\n",
"Je vous conseille d'écrire quasi tout le temps le nom des arguments pour éviter ce genre de confusion ; sauf quand il s'agit d'un argument obligatoire évident comme dans `plt.plot(x,y)`. \n",
"\n",
"Ou bien, conseil plus simple: adopter dans un premier temps la façon dont sont codés ces TP. Quand vous serez des vieux routier du python, vous créerez votre propre style. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## lois continues classiques"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### paramètres de localisation et d'échelle\n",
"\n",
"Toutes les lois dans scipy ont un paramètre de localisation `loc` que nous notons ici $\\mu$ et un paramètre d'échelle `scale` que nous notons ici $\\sigma$. Leur interprétation est la suivante :\n",
"\n",
"Si l'appel de `stats.xxx.rvs()` renvoie une v.a $X$\n",
"alors `stats.xxx.rvs(loc=mu,scale=sigma)` renvoie une v.a ayant la même loi que sigma $\\sigma X + \\mu$. Ainsi ces deux paramètres effectue à des translation et dilatation de la densité comme l'indique la proposition suivante :\n",
"\n",
"\n",
"\n",
"\n",
"***Proposition :*** si $x\\to f(x)$ est la densité d'une va $X$, alors la densité de $\\sigma X + \\mu$ est:\n",
"$$\n",
" \\frac 1 \\sigma \\ f \\ \\Big( \\frac{ x-mu} \\sigma \\Big)\n",
"$$\n",
"\n",
"\n",
"*Astuce:* Pour ne pas s'encombrer la mémoire, retenez uniquement les densités des lois dans le cas $\\mu=0$ et $\\sigma=1$. Par exemple: \n",
"\n",
"$$\n",
"\\begin{array}{cc}\n",
"a & b \\\\\n",
"\\end{array}\n",
"$$\n",
"\n",
"| nom de la loi |&nbsp; &nbsp; &nbsp; &nbsp; simplifié &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; complète &nbsp; &nbsp; &nbsp; &nbsp; |\n",
"|---------------|-----------| --------|\n",
"| exponentielle | $e^{-x} 1_{\\{x>0\\}}$ | $\\frac {1} {\\sigma} \\exp(- \\frac {x-\\mu } {\\sigma} )$ |\n",
"| normale | $\\frac {1} { \\sqrt {2 \\pi}} e^{-\\frac{1}{2} x^2}$ | ... |\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"*Démo de la proposition:*\n",
"Considérons $\\phi$ fonction teste et $X$ une va de densité $f$\n",
"$$\n",
" \\mathbf E[\\phi( \\sigma X + mu )] = \\int \\phi( \\sigma x + \\mu) \\ f(x) \\ dx \n",
"$$\n",
"On effectue le changement de variable $\\sigma x + \\mu \\to y$ \n",
"$$\n",
" \\mathbf E[\\phi( \\sigma X + mu )] = \\int \\phi( y) \\ f(... ) \\ dy ... \n",
"$$\n",
"On en déduit que ... \n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Loi Normale\n",
"\n",
" norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/vigon/Library/Python/3.6/lib/python/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
" warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD8CAYAAACb4nSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3Xl8VOXZ//HPNZOEVREkyhL2TUEQIQTcrVU2Eawrtir+akVbtz62Vq2ttvpoXZ7a9rH2Udxa64K4RwQBFbcqmLCvgQACQXZQ9iQz5/r9cQYdYyATMpN7luv9es0rc87cZ+Y7kFxzz33OuY+oKsYYYzJDwHUAY4wx9ceKvjHGZBAr+sYYk0Gs6BtjTAaxom+MMRnEir4xxmQQK/rGGJNBrOgbY0wGsaJvjDEZJMt1gKpatmypHTt2dB3DGGNSyqxZs7aoam5N7ZKu6Hfs2JHi4mLXMYwxJqWIyOpY2tnwjjHGZBAr+sYYk0Gs6BtjTAaxom+MMRkkpqIvIkNFpERESkXktoO0u0BEVETyo9bdHtmuRESGxCO0McaYQ1Pj0TsiEgQeBc4GyoAiESlU1cVV2h0G3ATMjFrXExgN9ALaAO+KSHdVDcfvLRhjjIlVLD39AqBUVVeqagUwHhhVTbt7gAeAfVHrRgHjVbVcVVcBpZHnM8YY40AsRb8tsDZquSyy7hsi0g9op6pv13ZbY1JCqBwq9/q3cKXrNMYcsjqfnCUiAeBh4Mo6PMdYYCxA+/bt6xrJmPjwwlAyGWb8H6z+5Nv1wQbQ+yIYdC206u0unzGHIJaivw5oF7WcF1m332HAccAHIgLQCigUkZExbAuAqo4DxgHk5+fbldqNeyXvwOTfwFeroVl7OPXX0KCp/9j2L2D+BJj7HHQ6DUb+HZp3cBrXmFjFUvSLgG4i0gm/YI8Gfrz/QVX9Gmi5f1lEPgB+rarFIrIXeEFEHsbfkdsN+Dx+8Y1JgJmPw+Rb4ehecNG/4JgREKzyp3LWH2D2s/Dxn+HJs+DHL0Hbfi7SGlMrNY7pq2oIuB6YAiwBJqjqIhG5O9KbP9i2i4AJwGLgHeA6O3LHJC0vDO/c7vfwewyHq6ZBr/O+X/ABGjWHk2/y22Q3hH+eA0sn1X9mY2pJVJNrNCU/P19twjXjxFs3wax/wsCfw5B7IRCMbbtdm+CFS+DLOXDJc3DsiITGNKY6IjJLVfNramdn5BoDMOtffsE/5b9g2P2xF3yApkfBlROhTV944+ewpTRhMY2pKyv6xqybDZNugc4/gDN/f2jPkdMELn4WAlnw0mVQsTu+GY2JEyv6JrPt2QYTxvi99Queql0Pv6oj2sOFT8HmpVB4IyTZ0KkxYEXfZLrCG2DXBrj4X9DkyLo/X5cz4czfwcJXYO7zdX8+Y+LMir7JXMunwdKJcMZt0LZ//J73lJuh3SCYdifs3R6/5zUmDqzom8xUuc8fxz+yK5x4Q3yfOxCAc/7HL/jv3xvf5zamjqzom8z06SOwfRWjn/sSyW6AiMT31roPTy7MguKnYP081+/WmG8k3YXRjUm4r9b4Z9IeO5KX/vgcHW6dmJCX+fVfR/Czgi7w9q/hp1P8bwDGOGa/hSbzTP09iMCQ+xL6Ml+XA2f9Eco+hwUTEvpaxsTKir7JLBsXweI34MTr4Ih2Nbevq+Mv9Wfi/PBBCIcS/3rG1MCKvsksHz0EOYfBoF/Uz+sFAnD6rbBtBSx6rX5e05iDsKJvMsempbDoDRg4Fhq3qL/X7XEOHNXL7+17Nt+gccuKvskcHz0E2Y1h0HX1+7qBAJz+G9i6HBa9Xr+vbUwVVvRNZti8DBa+CgVXx+fM29o6diTkHuN/8Hhe/b++MRFW9E1m+PjPkN0ITorziVixCgTgtFv8eXmWFLrJYAxW9E0m2LHenwun/5XQpGWNzROm14+gRWf47FF3GUzGs6Jv0t+sZ/wdqAVXu80RCELBWP+4/S/nuM1iMlZMRV9EhopIiYiUisht1Tx+rYgsEJG5IvKJiPSMrO8oInsj6+eKyGPxfgPGHFSoAoqfgW6D/V62a31/DNlNYOY410lMhqqx6ItIEHgUGAb0BC7dX9SjvKCqvVW1L/Ag8HDUYytUtW/kdm28ghsTk8VvwO5N/mGayaBhM+h7qb9TefcW12lMBoqlp18AlKrqSlWtAMYDo6IbqOqOqMUmgF09wiSHmY/7M2l2PtN1km8VjIVwuX95RmPqWSxFvy2wNmq5LLLuO0TkOhFZgd/TvzHqoU4iMkdEPhSRU+uU1pjaWDcL1hX7RTaZJjvL7QGdz4Dip21qBlPv4vaXoKqPqmoX4Fbgd5HV64H2qnoCcDPwgogcXnVbERkrIsUiUrx58+Z4RTKZbuY4yGnqz3/jQjD7gFMvj7x3EuxYx4W9Gx3S1M2t89q7eU8m5cUytfI6IHpmqrzIugMZD/wfgKqWA+WR+7Mi3wS6A8XRG6jqOGAcQH5+vg0Nmbrbu90/+7Xf5dDwe/2M+hGuPOC0zQvxKNNfctMFrSiu/G2tn3r1AyPqms5kqFh6+kVANxHpJCI5wGjgO2eXiEi3qMVzgOWR9bmRHcGISGegG7AyHsGNOagFr/jj5v2ucJ2kWh4BXg6dzsmBRbTFvt2a+lNj0VfVEHA9MAVYAkxQ1UUicreIjIw0u15EFonIXPxhnDGR9acB8yPrXwGuVdVtcX8XxlQ15zk4uje0Pt51kgN61TuNgCgXBD92HcVkkJiunKWqk4BJVdbdGXX/pgNs9yrwal0CGlNrGxbC+rkw9AHXSQ6qTHP5JNyLi4If8kj4PNTOlTT1wH7LTPqZ+zwEc6DPxa6T1GhC+AzaBTYzKLDEdRSTIazom/QSqoD5L0GPYfU7Z/4hmuINYIc25qLgh66jmAxhRd+kl2XvwJ6tcMLlrpPEpJwcCsMnMizwOYexx3UckwGs6Jv0Muc5OKw1dEmiM3Br8HL4dBpJBSOCn7mOYjKAFX2TPnZtgtJ34fjR/oyWKWKedmGZ19aO4jH1woq+SR+L3gANQ+/k34H7XcIb4ZPJDyyzY/ZNwlnRN+lj4Sv+BciPrjoJbPIr9E4C4Fwb4jEJZkXfpIftX8DamdD7AtdJDkmZHsUsrxujgp+6jmLSnBV9kx4WRs4BPC41iz5AYfgkjg2soZuUuY5i0pgVfZMeFrwKeQXQvKPrJIfs7fAgwiqMtN6+SSAr+ib1bVwMmxZB74tcJ6mTLTTjP95xjAx8il2HyCSKFX2T+ha+AhKEXue5TlJnhd5JdAhsoq+scB3FpCkr+ia1qfrTKHc+HZoe5TpNnU0JD6BcsxkV/I/rKCZNWdE3qe3L2fDV6pTegRttJ42Z7vVleHAmguc6jklDVvRNalv8JgSyoMdw10niZlJ4IEfLV/ST5a6jmDRkRd+khNZ57au9VuyKt/7C5JJ9SJMjD+las8noPe8EyjWb4cHPXUcxaSimi6gY49qGdWu/d73ZXrKKLg3u4PHDrqHDrT84pOdNxmvN7qYRH3p9GBacyX+HfmIXVzFxFdNvk4gMFZESESkVkduqefxaEVkgInNF5BMR6Rn12O2R7UpEZEg8w5vMNjw4k5AGmBbu7zpK3E0KD6SNbLOjeEzc1Vj0Ixc2fxQYBvQELo0u6hEvqGpvVe0LPAg8HNm2J/6F1HsBQ4F/7L9QujF1owwPzORTrxfbOdx1mLh7z+tHhQYZZkM8Js5i6ekXAKWqulJVK4DxwKjoBqq6I2qxCd+eWTIKGK+q5aq6CiiNPJ8xdXKMrKVTYCOTvfT8ddpJYz72+jA8OBM7UcvEUyxFvy2wNmq5LLLuO0TkOhFZgd/Tv7E22xpTW8ODMwirMDWc7zpKwkz2CsiTLfSRla6jmDQStz1EqvqoqnYBbgV+V5ttRWSsiBSLSPHmzTafuKmJck5gJjO8nmylmeswCTM13J9KDdpRPCauYin664B2Uct5kXUHMh7Yfz58TNuq6jhVzVfV/Nzc3BgimUzWVdbRJbA+bYd29ttBU/7jHcfQwOfYEI+Jl1iKfhHQTUQ6iUgO/o7ZwugGItItavEcYP9ZJYXAaBFpICKdgG6AdVtMnQwJFAOk9dDOflO8fDoGNtJD1tbc2JgY1Fj0VTUEXA9MAZYAE1R1kYjcLSIjI82uF5FFIjIXuBkYE9l2ETABWAy8A1ynquEEvA+TQYYEi5jtdWUTzV1HSbh3w/3xVL75oDOmrmI6OUtVJwGTqqy7M+r+TQfZ9l7g3kMNaEy01mylT2AV91eOdh2lXmzmCGZrNwYHi/nf8Pmu45g0YKf6mZQyOOj3eKd4AxwnqT9TwvkcF/iCPLGDHEzdWdE3KWVIoIjlXltWaWvXUerNVM/fdzHYhnhMHFjRNynjCHZSEFjKFC/9d+BGW62tWOq1++ZbjjF1YUXfpIwfBuaQJR5TwpkztLPfFC+fAbKUFuyoubExB2FF36SMIcEivtQWLNBOrqPUu6nhfIKi/DA423UUk+Ks6JuU0CgLTg0siBybn5zz4CfSIu1ImbZkSKDIdRST4qzom5QwuEsWjaTim52amUeYFu7PKYGFNGKf6zAmhVnRNylhZI8svtbGfO4d4zqKM1O9fBpKJacGFriOYlKYFX2T/LwwI7pnMd3rSyiDL/ZW5PXga23M2YFZrqOYFGZF3yS/siKOahLg3TS8QlZthPA/+M4MziGQebs1TJxY0TfJb+nbVISVD73jXSdxblo4nyNlJyfm2QXozKGxom+SX8lkPvgizE4au07i3IdeHyo0yMgemTvMZerGir5JbluWw9blvFlS6TpJUthFY2Z4PRllRd8cIiv6JrmV+JO7vlUSchwkeUzz+tOjZdD/QDSmlqzom+S2dBK06sPaHXblqP2+2aG99G23QUxKsqJvktfuLbB2JhxzjuskSWU9RzLry/A334KMqQ0r+iZ5LZsCKHQf6jpJ0ilcVglrP4ddNse+qZ2Yir6IDBWREhEpFZHbqnn8ZhFZLCLzReQ9EekQ9VhYROZGboVVtzXmgEomweFtobUdqllVYUkIUFg+1XUUk2JqLPoiEgQeBYYBPYFLRaRnlWZzgHxV7QO8AjwY9dheVe0buY3EmFhU7oMV7/u9fLEzkaqau8HzPxBtiMfUUiw9/QKgVFVXqmoFMB4YFd1AVaer6p7I4gwgL74xTcb54mOo3AM9hrtOkry6D4UV0/0PSGNiFEvRbwusjVoui6w7kKuAyVHLDUWkWERmiMh5h5DRZKKSSZDdBDqe4jpJ8uoxDCp3+x+QxsQormd4iMhlQD5wetTqDqq6TkQ6A++LyAJVXVFlu7HAWID27dvHM5JJRapQ8g50PROyG7pOk7w6nup/MJZMhm5nu05jUkQsPf11QLuo5bzIuu8QkbOAO4CRqlq+f72qrov8XAl8AJxQdVtVHaeq+aqan5ubW6s3YNLQ+nmw80sb2qlJdkP/g7Fksv9BaUwMYin6RUA3EekkIjnAaOA7R+GIyAnA4/gFf1PU+uYi0iByvyVwMrA4XuFNmiqZDAh0G+w6SfLrPsz/gFw/z3USkyJqLPqqGgKuB6YAS4AJqrpIRO4Wkf1H4zwENAVernJo5rFAsYjMA6YD96uqFX1zcMsmQ7uB0KSl6yTJr/sQQGDZO66TmBQR05i+qk4CJlVZd2fU/bMOsN2nQO+6BDQZ5ut1fq/1rD+4TpIamrSEdgX+ju8zvncKjTHfY2fkmuSyv8fafZjbHKmkxzD/g/Lr7+1qM+Z7rOib5FIyGVp0htwerpOkjv07vG2Ix8TAir5JHuW7YNWHfi/fzsKNXcvu0LxTZAe4MQdnRd8kj5XTIVzhD1eY2In4vf1VH/kfnMYchBV9kzxKJkPDI6D9INdJUk+PYRAu9z84jTkIK/omOXhhf0y629kQzHadJvW0HwQNm9kQj6mRFX2THMqKYM9WG9o5VMFs/2S2Ze/4H6DGHIAVfZMcSiZDIAu6VnvKh6kqmI2IfOd2yV3/gj1bOalDg+89FuutdZ7NfZXu4jrhmjGHrGSyP6Nmw2auk6SGcCUdbp34nVWL2UOlXsPlY0bzZejSQ3ra1Q+MiEc6k8Ssp2/c27oCtpTYCVl1tJPGzPSO4azAbNdRTBKzom/c27/zsYddC7eu3vX60y2wjo6y3nUUk6Ss6Bv3SibBUb2geUfXSVLeu15/AOvtmwOyom/c2r0V1nwGx9jc+fFQprks8dpzdnCW6ygmSVnRN24tnwLq2QVT4miq1598KaE5O1xHMUnIir5xq2QSHNYa2nzvgmrmEE0L9ycoypmBua6jmCRkRd+4U7kPSt/3T8iyCdbiZqF2Yr22sCEeUy0r+sadVR9C5W7ocY7rJGlGeDfcj9MC82lAheswJsnEVPRFZKiIlIhIqYh87/I8InKziCwWkfki8p6IdIh6bIyILI/cxsQzvElxS9+GnMOg06muk6SdaV5/Gks5JwcWuo5ikkyNRV9EgsCjwDCgJ3CpiPSs0mwOkK+qfYBXgAcj27YA7gIGAgXAXSLSPH7xTcryPH+emK4/hKwGrtOknRleT3ZqI84O2BCP+a5YevoFQKmqrlTVCmA8MCq6gapOV9U9kcUZQF7k/hBgmqpuU9XtwDTAzsAx8OVs2LURjrGhnUSoIJsPveM5KzgbwXMdxySRWIp+W2Bt1HJZZN2BXAXsn9+1ttuaTLF0IkjQJlhLoKnh/uTK15wgpa6jmCQS1x25InIZkA88VMvtxopIsYgUb968OZ6RTLJaMtGfYK1xC9dJ0tYHXl8qNcjgYLHrKCaJxFL01wHtopbzIuu+Q0TOAu4ARqpqeW22VdVxqpqvqvm5ubmxZjepavMy2Locjj3XdZK0toMmfOb1ZEigCFDXcUySiKXoFwHdRKSTiOQAo4HC6AYicgLwOH7B3xT10BRgsIg0j+zAHRxZZzLZ0rf8n3YWbsJN8QbQKbCR7lLmOopJEjUWfVUNAdfjF+slwARVXSQid4vIyEizh4CmwMsiMldECiPbbgPuwf/gKALujqwzmWzJRGjTD5rZ7p1Emxb2J2Dze/vGxHgRFVWdBEyqsu7OqPsH3Bunqk8DTx9qQJNmvl7nH7nzwztrbmvqbBPNme11ZXCwmEfC57uOY5KAnZFr6tfSt/2fx9h4fn2ZEh5A78AXtMUOkjBW9E19WzoRWnaH3O6uk2SMKV4+gB3FYwAr+qY+7dkGX3wCx9h1WOvTF9qaEi+PIVb0DVb0TX1aNgU0DMda0a9vU7x8BshSWtgc+xnPir6pP0vegsPb+kfumHo1JTyAoChn2XTLGc+Kvqkf5Tuh9F04dqTNne/AIu3IGi+X4YHPXUcxjlnRN/Vj2RQIl0PPUTW3NQkgTPIGcnJgIYezy3UY45AVfVM/Fr8JTVtBu4Guk2SsyeECsiXM2YHZrqMYh6zom8Sr2A3Lp/lz7QTsV86VedqFdXokQ4M2xJPJ7C/QJN7yaRDaa0M7zgmTwwWcFphPU/bU3NykJSv6JvEWvwmNW0KHk1wnyXiTwgNpICHODMxxHcU4YkXfJFblXn8n7rHnQiDoOk3Gm6Nd2aDNGW5DPBnLir5JrNL3oHK3De0kCSXA5HABZwTm0ph9ruMYB6zom8Ra/AY0au5fJcskhcnhAhpKpQ3xZCgr+iZxKvZAyWT/hKxgtus0JqJYe7BRj2BEcIbrKMYBK/omcZZPhYpdcNwFrpOYKB4B3g4P4geBuRxmR/FkHCv6JnEWvgpNjrKhnST0VvhEGkglZwds5s1ME1PRF5GhIlIiIqUicls1j58mIrNFJCQiF1Z5LBy5hOI3l1E0GWDfDr+n3+tHdtROEpqjXSnTlpwb/Mx1FFPPaiz6IhIEHgWGAT2BS0WkZ5Vma4ArgReqeYq9qto3chtZzeMmHZVMhtA+G9pJWsJb4RM5JbCQ5jbdckaJpadfAJSq6kpVrQDGA985/k5Vv1DV+YCXgIwmFS18FZq1g7wBrpOYA3grfCLZEmZo0C6ankliKfptgbVRy2WRdbFqKCLFIjJDRM6rVTqTUlrntUdEaNFIqFz6Dg9OKkWCQUSkzjcTf4u1Ayu81pwbsCGeTJJVD6/RQVXXiUhn4H0RWaCqK6IbiMhYYCxA+/bt6yGSSYQN69bS4daJXBycTnbwCT7Kf4gO/TvH5blXP2BX24o/YaJ3IjcEXyeX7WymuetAph7E0tNfB7SLWs6LrIuJqq6L/FwJfACcUE2bcaqar6r5ubm5sT61SVKjAp+yyjuahdrJdRRTg8LwiQRE7Zj9DBJL0S8CuolIJxHJAUYDMR2FIyLNRaRB5H5L4GRg8aGGNcmvFVs5MbCYN72TARuWSXYrtC0LvY78KPiJ6yimntRY9FU1BFwPTAGWABNUdZGI3C0iIwFEZICIlAEXAY+LyKLI5scCxSIyD5gO3K+qVvTT2HnB/xAQ5fWwHZufKl4Pn0KfwCq6SMxf4E0Ki2lMX1UnAZOqrLsz6n4R/rBP1e0+BXrXMaNJIT8KfkKx153V2sp1FBOjwvBJ3J71AucHP+Z912FMwtkZuSZu+rYK0CNQZr38FLOZI/jY682o4Kc2IJcBrOibuLm8TzblmsXE8CDXUUwtvR4+lTzZwmkd7OzpdGdF38RHOMSPe2cz3TuBr2nqOo2ppalef3ZqI6443mZDTXdW9E18rPyAVk0DNrSTovbRgHfCA7iwZ7Y/JbZJW1b0TXzMH8+2vcp0r6/rJOYQveadyuENBEom1dzYpCwr+qbu9n4FS95i/MJKKrDhgVQ1wzuW1V95MOc511FMAlnRN3W34GUI7ePJ2RWuk5g6UAI8M7cSVn4AX61xHcckiBV9U3ezn4VWfZizwSZZTXXPzI18cM953m0QkzBW9E3dfDkXNsyHfle4TmLiYM3XCl1+4A/xeGHXcUwCWNE3dTPn35DVEHpfWHNbkxr6XQE7ymDldNdJTAJY0TeHrnIvzH8Zjh0JjWxa3rTRYzg0auEP25m0Y0XfHLrFhVD+tQ3tpJusBnD8pbB0Euze4jqNiTMr+ubQzX4WmneCjnZCVtrpdzl4lTDvRddJTJxZ0TeHZtMSWP0J9B8DdjnD9HPUsdBuIBQ/DZ4dlZVOrOibQ1P0JAQbwAk2tJO2BlwN21bCSptwOZ1Y0Te1t28HzBsPx10ATY50ncYkSs9R0OQo+PwJ10lMHFnRN7U3bzxU7IKCn7lOYhIpK8cfvls2BbZ/4TqNiZOYir6IDBWREhEpFZHbqnn8NBGZLSIhEbmwymNjRGR55DYmXsGNI6pQ9AS06Qdt+7tOYxKt//8DCfhj+yYt1Fj0RSQIPAoMA3oCl4pIzyrN1gBXAi9U2bYFcBcwECgA7hIRO6A7la36ELYsg4KrXScx9aFZWzhmuH+kVuVe12lMHMTS0y8ASlV1papWAOOBUdENVPULVZ0PVN3NPwSYpqrbVHU7MA0YGofcxpXPn/BP3Ol1vuskpr4UjIW922Hha66TmDiIpei3BdZGLZdF1sWiLtuaZLNtlT/Xev8xkN3QdRpTXzqeCrnHwox/+MN7JqUlxY5cERkrIsUiUrx582bXccyBfPYoSBAKrnGdxNQnETjxOti4EFbY4ZupLpaivw5oF7WcF1kXi5i2VdVxqpqvqvm5ubkxPrWpV3u2+TMv9rkYDm/tOo2pb30uhqat4NNHXCcxdRRL0S8CuolIJxHJAUYDhTE+/xRgsIg0j+zAHRxZZ1JN0ZMQ2gsn3eA6iXEhqwEMvMafeXP9fNdpTB3UWPRVNQRcj1+slwATVHWRiNwtIiMBRGSAiJQBFwGPi8iiyLbbgHvwPziKgLsj60wqqdwLMx+HboP90/NNZsr/KeQ0td5+iotpTF9VJ6lqd1Xtoqr3RtbdqaqFkftFqpqnqk1U9UhV7RW17dOq2jVyeyYxb8PURuu89ohIzLdrTmwGe7Zwxh2vH7SdSXONjoB+Y2Dhq/DV2prbm6SU5TqAqX8b1q2lw60TY2obwOPWnF8zz2vMF6PvoQMHLu6rHxgRr4gmWQ36Ocx8zD+SZ+ifXKcxhyApjt4xyWtE4DM6BzbwWOhcOEjBNxniiHb+Tt3iZ2DXJtdpzCGwom8OKIDHTVmvscRrxzveANdxTLI47RYIl8N//uY6iTkEVvTNAZ0b+JQugfX8LXQBar8qZr8ju0CfS6DoKdi50XUaU0v2l2yqFcDjxqzXWeK1Z4qX7zqOSTan3QLhCvj0f10nMbVkRd9Ua2Skl//X0PnWy88kwezYjupq2ZV/ztnLno8eoVXTQEzbtM5r7/rdGezoHVONIGFuiPTyp1ovP7OEK2M+susZ2cBlWb/m3l9ezD2hy2tsb0d3JQfrwpnvuTj4AV0C6/mLjeWbg1itrXgtfCqXBaeRJ3YkT6qwv2jzHU3Yy81ZL/O518N6+aZGD4cuxCPAb7Jech3FxMiKvvmOa7LeIld2cF/lT7Dj8k1NNnAkT4SHMzL4GX2l1HUcEwMr+uYbrdjK1cFJFIZPZK52dR3HpIjHQ+eyWQ/nt9nPAzbffrKzom++8auslwng8WDoEtdRTArZTSP+ErqIgkAJQwJFruOYGljRNwD0lpVcEPyYZ8JDKdOjXMcxKeal8Bks89ry26wXaECF6zjmIKzoG4KEuS/7STbTjEdD57mOY1JQmCB/CI2hQ2AT12W94TqOOQgr+oYrglPpHfiCuyuvYCeNXccxKepT7zheD5/MtcG36CKxXlzP1Dcr+hmuFVv5VdbLfBA+nre9ga7jmBR3b+Vl7KUB92Y/je3UTU5W9DPcXdnPEsTjd6H/hx2iaepqC834U+jHDAos4YLAx67jmGrEVPRFZKiIlIhIqYjcVs3jDUTkpcjjM0WkY2R9RxHZKyJzI7fH4hvf1MWQwOcMCxbxv6HzbeetiZuXwmdQ5HXnjuznyGW76zimihqLvogEgUeBYUBP4FIR6Vml2VXAdlXtCvwFeCDqsRWq2jdyuzZOudNebS9pWJsbQC7b+VP2k8zzOvNEeLjjd2vSiRLg1sqxNKKCB7PHYcM8ySWWCdcKgFJVXQkgIuOBUcDiqDajgD9E7r8C/F3soql1UptLGtbW6gdG8FD2OBpRwX9V/oKQzbtn4myltuG+0I+5J/ufXOa9y3Phs13P0GiYAAAMf0lEQVRHMhGxDO+0BaKvglwWWVdtG1UNAV8DR0Ye6yQic0TkQxE5tY55TRz8YkA2ZwTncW/oJ6zUNq7jmDT17/DZfBA+njuynqezfOk6jolI9I7c9UB7VT0BuBl4QUQOr9pIRMaKSLGIFG/evDnBkTJbVynjobMbMj18PM+Fz3Idx6Q14ZbKsewlh79mP0pO0HUeA7EV/XVAu6jlvMi6atuISBbQDNiqquWquhVAVWcBK4DuVV9AVcepar6q5ufm5tb+XZiYHMYexmU/zI5y5TeVY7GjdUyibaY5t1aOpU9gFY8Ma+g6jiG2ol8EdBORTiKSA4wGCqu0KQTGRO5fCLyvqioiuZEdwYhIZ6AbsDI+0U1tCB4PZ/+DdrKZi17ey2aau45kMsQ0L5+/h0Yxtn8OFD/jOk7Gq7HoR8borwemAEuACaq6SETuFpGRkWZPAUeKSCn+MM7+wzpPA+aLyFz8HbzXquq2eL8JU7Mbgm9wdnA294Qu45M1YddxTIZ5OHQR75SGYNItsNYmZXMppsM2VHUSMKnKujuj7u8DLqpmu1eBV+uY0dTR4EARv8x6lVfDp/JseDDwiOtIJsN4BPjxq3vYdn9XmHA5/OxdaJbnOlZGsjNy01yBLOGR7L8zV7vw28qrsHF848r2fcDoF6BiN/z7fNhjX/pdsKKfxo6RNTyZ82fW6FH8tOIWyslxHclkuqN7waUvwvYv4IWL/Q8AU6+s6KepdrKRZ3PuZxcNuaLiNr7iMNeRjPF1PAUufArWzYKXr4SQzb9fn6zop6Euso4JOfeQTYgrKm5j/TfnyRnjUDD72+lAeo7k6sLdsHwqb19xBI2yD31akdZ57V2/s5Ri59+nmWNkDc/l3IcCoyt+R6nazjKTJMKV35laZBpwe+V73Nvtad677XiurvwVu2lU66dd/cCIOIZMf9bTTyP9ZBnjc+6hgiwurriLErUekEluL4Z/yM2VP6cgsJR/5/yJI9jpOlLas6KfJi4IfMSLOf/NV9qUiyvuYpW2dh3JmJi84Z3CdZU30ktWU5jzO7rL2po3MofMin6KC+Dx26zn+XPOYxR7PTiv4m7K1KayMKllilfAJRW/p4FU8lrOXZwVmOU6Utqyop/C2rCF57PvY2zW2zwTGsKYylvtKB2TsuZqV0aW/zcrtA3jsh/m9qznyaHSday0Y0U/JSmjAp/wToPb6B1Yya8qruWPoTE2L75JeRtpwcUVd/Ji+EyuyXqbN3N+Tw9Z4zpWWrGin2LaspnHsv/K33L+QYnmMaziT7zqneY6ljFxU04Od4Su4qcVv6alfEVhzu+4MfgaDbDj+ePBin6KaEAFNwRf490Gt3B6YB4PVI5mdMXvWatHu45mTEK87/VjaPkDTPXyuTn7Fd7NuYWzA8XY5RfrxsYDklwOlVwc/IBfZL1JG9nGxPBA7qv8CV/S0nU0YxJuK824ofJGXgj/kD9k/Ysnch5mpncMfw1dwGdeT2wuqdqzop+kDm8AVwbfYWzWRNrINoq97vyq8ud85vVyHc2YeveZ14tzKu7j0uD7/CKrkBdz7uVzrwePh0bwT6v7tWJFP5mowoYFUPw0624+jKbZz1LkdeeWymv4j3cc1qsxmSxEFv8OD2ZC+AwuDn7Az7MKeSrnz/z+xqbw8cPQ9ydwmA131sSKvmuqsGUZLHoDFr7i389qyIRFlbze80EWaGfXCY1JKuXk8O/wYF4Mn8nZgVlctP3PdHzvj/D+PdDxVDjuAjhmBDSxOaeqY0Xfhd1bYM1nsOJ9KH0XvloDiD/74KCfQ8/zuKrJkXQ41gq+MQcSIovJ3kAee3YPumkpLHjF7zi9dSO8dRO07Qddz4JOp/v3s2s/r086iqnoi8hQ4G9AEHhSVe+v8ngD4FmgP7AVuERVv4g8djtwFRAGblTVKXFLnwr2fgUbF/nDNhvmw9qZsLXUfyynKXQ+A075L+g+FA5v4zKpMakrtweceQf84Lewfh4sn+p3qD56CD58AALZ0KYv5A2Ao4+DVr39bbIauE5e72os+pELmz8KnA2UAUUiUqiqi6OaXQVsV9WuIjIaeAC4RER64l9IvRfQBnhXRLqravpcpLViN+zaCDs3wFdr4es1fs996wrYshx2b/q2beOW/i/dCZdBu0HQtj9k2YVNjIkbEb+4t+kLp//GvzrX2pmwZoZ/K34GQnsjbQNwRAdo2Q1adIEj2vmXcGyWB01bQZPctPz7jKWnXwCUqupKABEZD4wCoov+KOAPkfuvAH8XEYmsH6+q5cCqyIXTC4DP4hM/iip4IVAPvLD/U8Pf3vfC/uP7b+FKCFdEfpb790PlULkXQvugcg9U7PGLesVO2LcDynfAvq/9X6S929i1aQ1Nq/md2LjLY/k2j5KtHsu2eszf6DF3Q5gNu3YAK4GX4v72jTHVaNwCegzzb+DXga0rYOMC2LTE/9a9tRRWfwoVu76/faPm0KiF/zyNWkDDw6HB4f7PnKaQ08S/ZTWC7IaQ1dD/9hBsAMFsCOb4PwNZ3/4MZIEEIRCI/Az6H0ASWQ4mdtQ9lmdvC0RPe1cGDDxQG1UNicjXwJGR9TOqbNv2kNMezO4t8D9dE/LUZDX89j+6YTO/B5DbgyfeWU55/zFs0iPYRHO+1CNZpy0pz8qBo/BvEQ2ADrV4SZsj3JgECAQht7t/i6YK+77yv63vWOd/c9+1yf8Wv3eb39Hb+SVsXgrlO/0OoBeKf762/eHq9+P/vFFE9eBnt4nIhcBQVf1ZZPlyYKCqXh/VZmGkTVlkeQX+B8MfgBmq+lxk/VPAZFV9pcprjAXGRhZ7ACV1eE8tgS112D5RLFftWK7asVy1k465OqjWPMVuLD39dUC7qOW8yLrq2pSJSBbQDH+HbizboqrjgHExZKmRiBSran48niueLFftWK7asVy1k8m5Ypl7pwjoJiKdRCQHf8dsYZU2hcCYyP0LgffV/wpRCIwWkQYi0gnoBnwen+jGGGNqq8aefmSM/npgCv4hm0+r6iIRuRsoVtVC4Cng35EdtdvwPxiItJuAv9M3BFyXVkfuGGNMiolpN7GqTgImVVl3Z9T9fcBFB9j2XuDeOmSsrbgMEyWA5aody1U7lqt2MjZXjTtyjTHGpA+bT98YYzJI2hZ9EfmViKiIJM3E8yJyj4jMF5G5IjJVRJzPuyAiD4nI0kiu10XkCNeZ9hORi0RkkYh4IuL0SAsRGSoiJSJSKiK3ucwSTUSeFpFNkcOmk4aItBOR6SKyOPJ/eJPrTAAi0lBEPheReZFcf3SdaT8RCYrIHBGZmMjXScuiLyLtgMFAsl1c8yFV7aOqfYGJwJ01bVAPpgHHqWofYBlwu+M80RYC5wMfuQwRNRXJMKAncGlkipFk8E9gqOsQ1QgBv1LVnsAg4Lok+TcrB85U1eOBvsBQERnkONN+NwFLEv0iaVn0gb8AvyHJrqumqjuiFpuQBPlUdaqq7j+1cAb+uRRJQVWXqGpdTtSLl2+mIlHVCmD/VCTOqepH+EfMJRVVXa+qsyP3d+IXs8ScjV8L6ts/30J25Ob871BE8oBzgCcT/VppV/RFZBSwTlXnuc5SHRG5V0TWAj8hOXr60X4KTHYdIglVNxWJ8wKWKkSkI3ACMNNtEl9kGGUusAmYpqrJkOuv+B1VL9EvlJLz6YvIu0Crah66A/gt/tCOEwfLpqpvquodwB2RKaevB+5ynSnS5g78r+TPJzpPbbOZ1CUiTYFXgV9W+abrTORcob6R/Vevi8hxqupsn4iIjAA2qeosETkj0a+XkkVfVc+qbr2I9AY6AfP8ST7JA2aLSIGqbnCZrRrP45/7kPCiX1MmEbkSGAH8UOv5GN5a/Hu5FNN0Iua7RCQbv+A/r6qvuc5Tlap+JSLT8feJuNwRfjIwUkSGAw2Bw0XkOVW9LBEvllbDO6q6QFWPUtWOqtoR/2t4v/oq+DURkW5Ri6OApa6y7Be5QM5vgJGqusd1niQVy1QkJkpkavWngCWq+rDrPPuJSO7+I9REpBH+dUKc/h2q6u2qmhepWaPxp7FJSMGHNCv6KeB+EVkoIvPxh6CS4TC2vwOHAdMih5I+5jrQfiLyIxEpA04E3hYRJ1ddi+zo3j8VyRJggqoucpGlKhF5Ef/6FD1EpExErnKdKeJk4HLgzMjv1dxIT9a11sD0yN9gEf6YfkIPkUw2dkauMcZkEOvpG2NMBrGib4wxGcSKvjHGZBAr+sYYk0Gs6BtjTAaxom+MMRnEir4xxmQQK/rGGJNB/j+w/UcdFEEnXAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(stats.norm.rvs(loc=0,scale=1,size=400),normed=True,edgecolor=\"k\")\n",
"\n",
"x=np.linspace(-4,4,100)\n",
"plt.plot(x,stats.norm.pdf(x,loc=0,scale=1));\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"EXO : Reprenez le dernier programme, améliorez-le car il souffre d'un défaut classique. \n",
"Faites varier les paramètres loc et scale. Supperposer plusieurs graphique pour que l'on comprennent bien les effets de dilatation et de translation de ces paramètres. \n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Paramètres de forme\n",
"\n",
"Pour toutes les loi suivantes, nous ne nous occuperons plus des paramètres loc et scale, pour nous concentrer sur les autres paramètres (quand ils existent). Ces autres paramètres sont appelé paramètres de forme. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Loi gamma\n",
"\n",
"\tgamma.pdf(x, a) = x**(a-1) * exp(-x) / gamma(a)\n",
"\n",
"Pour quelle valeur de `a` retrouve-t-on une loi exponentielle ?\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/vigon/Library/Python/3.6/lib/python/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
" warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"paramètre de forme\"\"\"\n",
"a=2\n",
"plt.hist(stats.gamma.rvs(a=a,size=400),normed=True,edgecolor=\"k\")\n",
"\n",
"x=np.linspace(0,8,100)\n",
"plt.plot(x,stats.gamma.pdf(x,a=a));\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exo: Le paramètre des forme est a. Quand il est entier il a l'interprétation suivante : gamma(a) est la loi de la somme de a v.a. exponentielle indépendantes. Illustrer ce fait par des simulations. \n",
"\n",
"Exo: pour quels paramètres a la densité est-elle monotone ? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Loi Beta\n",
"\n",
"\n",
" gamma(a+b) * x**(a-1) * (1-x)**(b-1)\n",
" beta.pdf(x, a, b) = ------------------------------------\n",
" gamma(a)*gamma(b)\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/vigon/Library/Python/3.6/lib/python/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
" warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\" deux paramètres de formes\"\"\"\n",
"a=2\n",
"b=2\n",
"plt.hist(stats.beta.rvs(a=a,b=b,size=400),normed=True,edgecolor=\"k\")\n",
"x=np.linspace(0,1,100)\n",
"plt.plot(x,stats.beta.pdf(x,a=a,b=b));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exo : faites varier a et b de manière à faire apparaitres tous les 'type' possible de loi béta : cloche, smiley ,décroissant, croissant"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lois à Queues lourdes\n",
"\n",
"Une loi est dites à queue lourde lorsque les v.a qui ont cette loi peuvent prendre, de temps en temps, des grandes valeurs positives ou négatives. Elle servent à modéliser des évènements rare et violent (ex: crue d'un fleuve). "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"\"\"\" une fonction effectuant un histogramme tronqué \"\"\"\n",
"def hist_trunc(ech,gauche,droite,nb_batons): \n",
" bins=np.linspace(gauche,droite,nb_batons)\n",
" interval_width=(droite-gauche)/nb_batons\n",
" weigh=np.ones_like(ech)/len(ech)/interval_width\n",
" plt.hist(ech,bins=bins,weights=weigh,edgecolor=\"k\")\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Loi t de Student\n",
"```\n",
" gamma((df+1)/2)\n",
" t.pdf(x, df) = ---------------------------------------------------\n",
" sqrt(pi*df) * gamma(df/2) * (1+x**2/df)**((df+1)/2)\n",
"```\n",
"\n",
"C'est une loi très utile en statistique. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD8CAYAAACb4nSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3Xl8VPW9//HXZ2aysK8RMIEAskgQBI2441K02Fqw99pWb+3V2/aiv5a6dYHa1vZqF2t729qHthWX3ttWi4rVSy0WrbhVBQmLQFhDWJJAMKxhyTZzPr8/zgkOISGTZJIzy+f5eMxjZs4y844On/nO93zP94iqYowxJj0E/A5gjDGm61jRN8aYNGJF3xhj0ogVfWOMSSNW9I0xJo1Y0TfGmDRiRd8YY9KIFX1jjEkjVvSNMSaNhPwO0NTAgQN1+PDhfscwxpiksmLFir2qmtPadglX9IcPH05RUZHfMYwxJqmIyI5YtrPuHWOMSSNW9I0xJo1Y0TfGmDRiRd8YY9KIFX1jjEkjVvSNMSaNWNE3xpg0YkXfGGPSiBV9Y4xJI1b0jYkyJG8YItLu25C8YX7/CcacUsJNw2CMnyorysif81K799/x02vjmMaY+LOWvjHGpBEr+sYYk0as6BtjTBqxom+MMWnEir4xxqQRK/rGGJNGrOgbY0waianoi8h0EdkkIiUiMreZ9beJyFoRWS0i/xSRAm/5cBGp8ZavFpHfxfsPMMYYE7tWT84SkSDwCHAVUA4sF5GFqro+arOnVfV33vYzgF8A0711W1V1UnxjG2OMaY9YzsidApSoaimAiMwHZgLHi76qVkdt3wPQeIY0xk/nywa+l/FHMmkAoFL7c3vDbA7Sy+dkxrRdLN07uUBZ1PNyb9kJROSrIrIVeBC4PWrVCBFZJSJvisilHUprTBcLEuHHGY8zUA6xRXMp0VwuDqxjduhFv6MZ0y5xO5Crqo+o6hnAHOC73uLdwDBVnQzcDTwtIr2b7isis0SkSESKqqqq4hXJmA77bPANzgjs5t6GW/hqw518peFOFkQu4wvBV8kT+6ya5BNL0a8AhkY9z/OWtWQ+cB2Aqtap6j7v8QpgKzCm6Q6qOk9VC1W1MCcnJ9bsxnSqbtRyZ+h5ipwxvOIUHl/+y/C/ogh3hZ7zMZ0x7RNL0V8OjBaRESKSCdwALIzeQERGRz39JLDFW57jHQhGREYCo4HSeAQ3prN9Mfh3BslBftJwIyDHl1cygN9HpvPpwDuMkx3+BTSmHVot+qoaBmYDi4ENwLOqWiwi93kjdQBmi0ixiKzG7ca52Vs+FVjjLV8A3Kaq++P+VxgTZ/2o5rbQX3klci4rdOxJ638bnkE13ZkTmu9DOmPaL6b59FV1EbCoybJ7ox7f0cJ+zwPPdySgMX64OfQK3anlwfDnml1fTQ8eDl/HdzOe4qxwKet0ZBcnNKZ97IxcY5oxLbCSIh1Liea1uM2CyFQiKlwVXNmFyYzpGCv6xjRxGgc4K7CdNyKnPqfwIL1YpaO5PLC6i5IZ03FW9I1p4vKgW8Rfd1o/kfz1yCTODpQykEOdHcuYuLCib0wTVwRWs0v7s1GHtrpt4xdD4xeFMYnOir4xUTICcElgnde1I61uv17z2aN9rYvHJA0r+sZEuWRYkF5SwxJncox7CK9HJjE1sJYQ4U7NZkw8WNE3JsonRoeo0xDvOuNj3ud1ZzK95RjnyJZOTGZMfFjRNybKJ0aHWOaM4xjZMe/zjjOeeg1ypfXrmyRgRd+YRge2U5ATjGnUTrQjdGe5c6b165ukYEXfmEZbXgViG6rZ1BJnEmcGyhjau/WDv8b4yYq+MY22vUXpAYftOqTNu77tTATgihExzWxijG+s6BvTqLyI98oi7dp1i+ZSrd04PzcY51DGxJcVfWMADlXA4V0srWjfsEslwAfOGVyQZ0XfJDYr+sYAVBQBsLS8fS19gFU6iomDAlB/LF6pjIk7K/rGAJQvh2AWH1Q67X6J1c4oQgGB3TaKxyQuK/rGAJQXwZCzaWh/zWe1M8p7reXxyWRMJ7Cib0ykAXatgrzzOvQy++lNyX7Hir5JaFb0jdlTDOFayDu3wy+1rDwC5SviEMqYzmFF35jGlnkHW/qAO/rn8C53NJAxCSimoi8i00Vkk4iUiMjcZtbfJiJrRWS1iPxTRAqi1n3b22+TiHw8nuGNiYvyIug5CPq0Pn9+a46P/rEuHpOgWi36IhIEHgGuAQqAG6OLuudpVZ2gqpOAB4FfePsWADcA44HpwG+81zMmcVQUua186fgUCh9UOhDMOj4E1JhEE0tLfwpQoqqlqloPzAdmRm+gqtVRT3sA6j2eCcxX1TpV3QaUeK9nTGI4th/2lUBux/vzAXf0z5Cz3V8PxiSgWIp+LlAW9bzcW3YCEfmqiGzFbenf3pZ9jfFNhXfQNQ79+cflneeOBoo0xO81jYmTuB3IVdVHVPUMYA7w3bbsKyKzRKRIRIqqqqriFcmY1pUvBwnA6bFeKSsGeYXuaKA96+L3msbESSxFvwKIPsKV5y1ryXzgurbsq6rzVLVQVQtzcnJiiGRMnFSshJxxkNUzfq/Z2FVUsTJ+r2lMnMRS9JcDo0VkhIhk4h6YXRi9gYiMjnr6SaDxunELgRtEJEtERgCjgfc7HtuYOKlc4/bBx1PfYZDd131tYxJMq5N/q2pYRGYDi4Eg8KSqFovIfUCRqi4EZovINKABOADc7O1bLCLPAuuBMPBVVW3/jFbGxNPhPXBkDwyeEN/XFXFfc7cVfZN4Yrrig6ouAhY1WXZv1OM7TrHvj4AftTegMZ2msSU+ZGL8X3vI2bD8cYiEIWgXVjGJw87INemrsejHu6UPMHiiezB335bWtzWmC1nRN+lr9xroNxyy+8T/tRt/PVgXj0kwVvRN+qpc0zmtfIABoyGUbQdzTcKxom/SU2017C+FwXEeudMoGILTCmD3B53z+sa0kxV9k54aT5zqjIO4jYZMdFv6qq1va0wXsaJv0lPlWvd+cCcW/cETofYQHCprfVtjuogVfZOedq+B7gOh1+DOe4/Gk77sYK5JIFb0TXqq/MDtfonDdMotOq3AndfHDuaaBGJF36SfcD18uLFzu3YAMru7o3ispW8SiBV9k36qNoDT0LkHcRs1Hsw1JkFY0TfppysO4jYaPBGqK+Dovs5/L2NiYEXfpJ/dayCjB/Q/o/Pfq/HXhLX2TYKwom/ST+VaGDQeAl3w8R9sRd8kFiv6Jr2ouidmddb0C0117w+9c6HSrqJlEoMVfZNeDu6AumoYfFbXveegs+zSiSZhWNE36aWxxT2oi1r64H7B7N0M4bque09jWmBF36SXPesAgUEFXfeeg84CJwxVG7vuPY1pgRV9k14q10L/kZDZo+ves/H4gfXrmwRgRd+klz3rurY/H9wvmVA369c3CSGmoi8i00Vkk4iUiMjcZtbfLSLrRWSNiLwmIvlR6yIistq7LYxneGPapLYaDmzv2v58gEDQ7U5qPCnMGB+1WvRFJAg8AlwDFAA3ikjTDtFVQKGqTgQWAA9GratR1UnebUacchvTdh+ud++7uqUPH43gsbn1jc9iaelPAUpUtVRV64H5wMzoDVT1dVU95j1dCuTFN6YxcdDY0h7kQ9EfPAFqDkD1rq5/b2OixFL0c4Hoq0CUe8ta8iXg5ajn2SJSJCJLReS65nYQkVneNkVVVVUxRDKmeUPyhiEizd4evf92DtQo0q/lbTpN4xeN9esbn4Xi+WIichNQCFwWtThfVStEZCSwRETWqurW6P1UdR4wD6CwsNB+/5p2q6woI3/OS82um5J5L5vIIH/O91rcf8dPr+2cYIPGu/eVa2HMxzvnPYyJQSwt/QpgaNTzPG/ZCURkGvAdYIaqHj8LRVUrvPtS4A1gcgfyGtMuARzGShkbnGH+BMjuDX3zraVvfBdL0V8OjBaRESKSCdwAnDAKR0QmA4/iFvwPo5b3E5Es7/FA4GJgfbzCGxOrfNlDd6ljvea3vnFHBDNa7Dp64b0SNr65oMX1IsKQPJ++lEzaaLV7R1XDIjIbWAwEgSdVtVhE7gOKVHUh8DOgJ/Cc1y+60xupMw54VEQc3C+YB1TVir7pcuNkB0Dnt/QjDS12L+0ILWBG8AXGznmeWrKa36azupeM8cTUp6+qi4BFTZbdG/V4Wgv7vQt08aBoY042LrCTsAbYov4NLNvg5BMMKWOljA90lG85THqzM3JNWhgnOyjVIdSR6VuG9er+yhgX2OlbBmOs6Ju0MC6wkw2d3Z/finLN4bB2O97VZIwfrOiblNeXw+TKPtY7/hZ9JcAGHUZBwIq+8Y8VfZPyGrtTinW4v0GAYmc442QnguN3FJOmrOiblDdetgNdMHInBus1n55SS77s8TuKSVNW9E3KKwjsoFL7sY8+fkc53sVUYP36xidW9E3KK5AdFDvD/Y4BwBbNo0GD1q9vfGNF36S0LOoZJRWdfyZujOrJoERzj3c5GdPVrOiblDZGygmJ4/vInWjrNd9a+sY3VvRNSmssrokwcqfReiefQXKQgRzyO4pJQ1b0TUobL9s5rN0o0xy/oxzX+AVUENjuaw6Tnqzom5RWENjBBh2GJtBHfb03dNRG8Bg/JM6/BGPiTHAYl0AjdxpV05NyHWj9+sYXVvRNyhoue+jRFXPot8N6J99G8BhfWNE3Kaux+2R9grX0wZ2OYYRU0o1av6OYNGNF36SsgsB2GjTIFs31O8pJ1ms+AVHOlDK/o5g0Y0XfpKzxsoMSzaWeDL+jnKTxvIHxNoLHdDEr+iZFKeMD2xOyPx+ggoEc1B4UWL++6WIxFX0RmS4im0SkRETmNrP+bhFZLyJrROQ1EcmPWneziGzxbjfHM7wxLRnEAXLkEGuckX5HaYGw1hnBhMA2v4OYNNNq0ReRIPAIcA1QANwoIgVNNlsFFKrqRGAB8KC3b3/g+8D5wBTg+yLSL37xjWnexEApAGudET4nadlaHclYKSOLer+jmDQSS0t/ClCiqqWqWg/MB2ZGb6Cqr6vqMe/pUqDx6tMfB15V1f2qegB4FZgen+jGtGxCoJSwBhK2ewdgjTOSTIkw1g7mmi4US9HPBaI/leXespZ8CXi5nfsaExcTZRtbNI9asvyO0qLGXyGNv0qM6QpxPZArIjcBhcDP2rjfLBEpEpGiqqqqeEYyaUmZEChN4P58VwUD2ae9mCDWr2+6TixFvwIYGvU8z1t2AhGZBnwHmKGqdW3ZV1XnqWqhqhbm5CTOxFgmOeWylwFymLWauP35LmGtM9Ja+qZLxVL0lwOjRWSEiGQCNwALozcQkcnAo7gF/8OoVYuBq0Wkn3cA92pvmTGdpnFETKK39AHW6AhGSznZ1LW+sTFx0GrRV9UwMBu3WG8AnlXVYhG5T0RmeJv9DOgJPCciq0VkobfvfuB+3C+O5cB93jJjOs3EQCn1GmSj+n8h9NasdUYSEsdm3DRdJhTLRqq6CFjUZNm9UY+nnWLfJ4En2xvQmLaaIKVs1qEJeSZuU42/RiYEtrEyMsbnNCYd2Bm5JuVMDJSyJoHH50fbQz8+1L7Wr2+6jBV9k1JG9hP6yDHWauL357uENc4IJogVfdM1rOiblFJ4ehBIjoO4jdY6Ixklu+hu0yybLmBF36SUc4cEqdMQm3Vo6xsniDU6koCoTb5muoQVfZNSCk8PskGH0RDbGIWEsO74mbl2kpbpfFb0TepwHM4dEjxeRJNFFX3Zpf05O7DV7ygmDVjRN6mjaiN9soWVzmi/k7TZKmcUk2WL3zFMGrCib1JH2TIAVmjyjXdf6YxhWKCKwT3F7ygmxVnRN6mj7H0+POqwQwf5naTNGn+dXJgX9DmJSXVW9E3qKFvGu2URIPlay8U6nDrN4KKhVvRN57Kib1LD0X2wfyvvlUf8TtIu9WSwRkdYS990Oiv6JjWUvw/gtfST0wpnjHtyWdhm3DSdx4q+SQ1lyyAQomhX8hb9Vc5oskICuz/wO4pJYVb0TWooex+GnE1t2O8g7Xd8qKk3CsmYzmBF3yS/SANUrISh5/udpEOq6MvW/Y77BWZMJ7Gib5Jf5VoI10DeeX4n6bB3y8JuS1/V7ygmRVnRN8mvsWWc5C19gHfLI3BkDxzc6XcUk6Ks6JvkV7YMeudBn1y/k3TYe42jj6yLx3QSK/om+ZW9D0On+J0iLtZ96EBmTzuYazpNTEVfRKaLyCYRKRGRuc2snyoiK0UkLCLXN1kX8S6WfvyC6cbEzcGdUF2eEl07ABEF8gph53t+RzEpqtWiLyJB4BHgGqAAuFFECppsthO4BXi6mZeoUdVJ3m1GB/Mac6Jtb7v3I6b6myOehl8Ke9a5ZxkbE2extPSnACWqWqqq9cB8YGb0Bqq6XVXXAE4nZDSmZdvegu4D4bRxfieJn8YvsO1v+5vDpKRYin4uUBb1vNxbFqtsESkSkaUicl2b0hlzKqpuYRxxKUjyTbLWotMnu/36297yO4lJQV1xTbl8Va0QkZHAEhFZq6onXCJIRGYBswCGDRvWBZFMSthfCtUVqdW1AxDMgPyLrKVvOkUsLf0KIPoq03nespioaoV3Xwq8AUxuZpt5qlqoqoU5OTmxvrRJd9vedO+Hp1jRB7dff+9mqN7tdxKTYmIp+suB0SIyQkQygRuAmEbhiEg/EcnyHg8ELgbWtzesMSfY9jb0Oh0GnOF3kvizfn3TSVot+qoaBmYDi4ENwLOqWiwi94nIDAAROU9EyoHPAI+KSLG3+zigSEQ+AF4HHlBVK/qm41TdPu8RU1OrP7/R4AmQ3fejXzPGxElMffqqughY1GTZvVGPl+N2+zTd711gQgczGnOyDzfAsb3uQdxUFAjC8Es+GpJqTJzYGbkmOW1PwfH5TY2YCgd3wIHtficxKcSKvklO296CvvnQN4VHew33fsVYa9/EkRV9k3yciDc+P4Vb+eCecNZ9oB3MNXFlRd8kn12roPYQjLzc7ySdSwRGXgZbl4BjJ7ub+LCib5LP5sUgATjjSr+TdL7RH4ejVbB7ld9JTIqwom8SypC8YYjIKW8rn/kJb22vR3oMOGldyhk1zf2C27zY7yQmRXTFNAzGxKyyooz8OS+1uH4Q+zknezY/abiR/DmfOmn9jp9e25nxul6PAZA3BTb/Ha64x+80JgVYS98klSuDbjfHEuek2TxSQzDjpF8vc3//Buz+gNN7BVr9FTQkL4VHM5m4sJa+SSpXBlZR5uSwRZP/0ojNijSc9EtnpZQBc/jC7XfzTOSKU+6ecr90TNxZS98kjSzquSSwjtecyUAK9t+3YLPmUa4D+Vhgpd9RTAqwom+SxoWB9XST+tTt2mmR8FpkMpcE1pFFvd9hTJKzom+SxpWBVRzVLJY5KXSVrBi97kymu9RxQWCD31FMkrOib5KEcmVwFe84Z1FHpt9hutx7TgHHNIsrAjZe33SMFX2TFMbJTvJkbxp27bjqyOQd5yymBVcC6ncck8Ss6Juk8Knge4Q1wCuRQr+j+GZRZAp5spdzZIvfUUwSs6JvkoDyqcB7vOOcxX56+x3GN68651KrGXwq+J7fUUwSs6JvEt5kKWFooIqFkYv8juKrI3RniTOZTwaXEcAmYDPtY0XfJLxPBd+jTjN4xUnfrp1Gf41cyGlykPNtFI9pJyv6JqEFcLg2uJTXnUkcprvfcXy3xJnMEc1mRuBdv6OYJBVT0ReR6SKySURKRGRuM+unishKEQmLyPVN1t0sIlu8283xCm7Sw/mBDZwmB1kYudDvKAmhjkxecQq5Jvg+GYT9jmOSUKtFX0SCwCPANUABcKOIFDTZbCdwC/B0k337A98HzgemAN8XkX4dj23SxacC73JEs9N2qGZzFkYupK8c5dLAGr+jmCQUS0t/ClCiqqWqWg/MB2ZGb6Cq21V1DZx0dOnjwKuqul9VDwCvAtPjkNukgQzCXBNc7o5aIcvvOAnjHWcCB7SnjeIx7RJL0c8FyqKel3vLYhHTviIyS0SKRKSoqqoqxpc2qe7ywGr6yRH+al07J2ggxMuRKVwdKKInx/yOY5JMQhzIVdV5qlqoqoU5OTl+xzEJ4t+Cr1Gp/XjTOdvvKAnnmcjl9JA6ZgbtgK5pm1iKfgUwNOp5nrcsFh3Z16SxPKnissAa5keuIELQ7zgJ5wM9g3XOcD4ffA2blsG0RSxFfzkwWkRGiEgmcAOwMMbXXwxcLSL9vAO4V3vLjDmlG4JLUGB++NQXDUlfwlORj1EQ2MEk2ep3GJNEWi36qhoGZuMW6w3As6paLCL3icgMABE5T0TKgc8Aj4pIsbfvfuB+3C+O5cB93jJjWpRBmM8F32CJcw6VDPA7TsJaGLmII5rN54P/8DuKSSIxXS5RVRcBi5osuzfq8XLcrpvm9n0SeLIDGU2auSpQRI4c4qnIx/yOktCO0o0XIxdzffAt7g/fRDU9/Y5kkkBCHMg1Jtrng69R5uTwljPR7ygJ76nINLKlgX8Nvu13FJMkrOibhDJmQICLg8X8OXIljn08W7VB81npjLIDuiZm9q/KJJSvX5hJnWbwbORyv6MkjT+Er2ZUYBdX2lW1TAys6JvEUb2LWyZl8EzkcvbSx+80SeMl5wLKnBxmh170O4pJAlb0TeJ492ECAvMi1/qdJKmECfFo5FrOCZRw+XA7p8GcmhV9kxiO7oMVv+epNQ2Uq52V3VbPRS6jSvtwzyU2R5E5NSv6JjEs+y001PDAO/V+J0lKdWTyWPgTXHVGCMpX+B3HJDAr+sZ/tYdg2TwYdy0b99plANvrqcg09tcovP3ffkcxCcyKvvHf0t9C3SG49Ot+J0lqR+nGr5fVw6a/wS4byWOaZ0Xf+Kt6N7zzEBTMhNPtQikd9culddB9ICz+DqiN2zcns6Jv/LXkfnDCMO2//E6SEqrrgCvugR3vwMaX/I5jEpAVfeOfXath9dNw/m3Qf4TfaVLHOTdDzpnwyvcgbAfGzYms6Bt/qMIr34Xu/WHqN/xOk1qCIbj6R3BgG7w/z+80JsFY0Tf+2PgSbH/b7YrItrNv4270NBg1Dd58EI7YJUjNR6zom65XcwD+9g0YdBacc4vfaVLXx38M4Rp4+Zt+JzEJxIq+6Xp/vweOVsF1v3G7IkznyBkLl82B4heg2OblMS4r+qZrbV4MHzztjskfYhc873QX3wlDJsHfvu5OdWHSnhV903VqDsJf74DTxsNU63LoFMEMROSjWyiDCff+k/rDVfz534eeuK6Z25C8YX7/BaaTxfTbWkSmAw8BQeBxVX2gyfos4A/AucA+4HOqul1EhuNeV3eTt+lSVb0tPtFNUlGFl+6CIx/CjX+GUKbfiVJTpIH8OSeOzz8M/Np5gW9MeI5lY+/gReeSFnff8VOb4TTVtdrSF5Eg8AhwDVAA3CgiBU02+xJwQFVHAb8Efhq1bquqTvJuVvBT3JC8Yc22IO+8MBuK/8LcV48iuee02NI0neO3kRksc87kJxmPc6bs9DuO8VEsLf0pQImqlgKIyHxgJrA+apuZwA+8xwuAh8X+Baelyoqyk1qa58lGfp75Q/4eOZf5l9xJ/iUtfzSspdk5IgSZXX87L2Xdw+8yfsmM+h9STQ+/YxkfxNKnnwuURT0v95Y1u42qhoFDwABv3QgRWSUib4rIpR3Ma5LMaRzgN5kPsUMH8c2GWwFrC/ilir58pf4OcmUv/53xWwSb0TQddfaB3N3AMFWdDNwNPC0ivZtuJCKzRKRIRIqqquxEklTRgxoey/xvelDLbQ13cZjufkdKeyt0LD8M38RVwZXMCc33O47xQSxFvwIYGvU8z1vW7DYiEgL6APtUtU5V9wGo6gpgKzCm6Ruo6jxVLVTVwpwcu2pSKsikgXkZv2C8bGd2w9fYonl+RzKe/41czR/CV3Fb6CVmBf/qdxzTxWIp+suB0SIyQkQygRuAhU22WQjc7D2+HliiqioiOd6BYERkJDAaKI1PdJOoAjj8KuMRLg4W882GW1ninON3JHMC4fvhm/lr5ALuyfgznwm+4Xcg04VaPZCrqmERmQ0sxh2y+aSqFovIfUCRqi4EngD+KCIlwH7cLwaAqcB9ItIAOMBtqrq/M/4QkxgCAg+EHuMTwfe5v+EmXnDsME4iUgLc3fAV+nCUB0KPUaNZvORc6Hcs0wViGqevqouARU2W3Rv1uBb4TDP7PQ8838GMJlmE63jm+m5cH3qTX4X/hScin/A7kTmFBkLc2nAX/5P5IL/OeJje4WP8xO9QptPZxCcmPuqOwDM3cX1BBvc33GQFP0nUkM2/18/lNxkP8eOMJ3AuznRPpLMR1ynLpmEwJ2jp5KpT3Yb2CbB89mAiJUu45cUaK/hJpo5Mbm24ixcjF/HAtGx3nh67+ErKspa+OUFzJ1edygWB9Tyc8WuyaGBWw1f43w++T/70TgxoOkWYEHc1fIXNS1/nWzwBe4rhs3+AXoP8jmbizFr6pl0Ehy8F/8afMn7MIe3BdfX38Zpzrt+xTAcoAea87nDDgmMcK32PXT8YxaX5oTb96rMJ2xKftfRNm+VSxc8yHuWi4HoWRwr5esNtHLETr1JDpIGl177Evzg7ebTHL3jzlirmRT7JL8PXU0frk+TZNBqJz1r6JmaCw2eDr/P3rLlMDJQyp+E/ubXhLiv4KWijDuMT9T9hfuQKbgu9xMLM7zJB7BSbVGBF38TkLCllQeZ/8WDGYxTrcKbXP8AzkSuwuXRS11G6cU/4y9xS/y36yhH+L/N7/Dj0GP2o9jua6QDr3jGnNIR93B76C58LvsE+evGNhlt5PnIpau2FtPGGM4lpdT/njtDz3Bx8hU8Gl/Hr8L/wp8i0mLp8TGKxom+alcMBvhJayL8FX0NQnoxM56Hwv9qkaWnqMN35YfgLzI9cwb2hP/K9jD/xn6G/8Uh4Js9ErqCeDL8jmhhZ0TcnKMgJ8L3QPD4dfIcgEZ6LXMYjkesoV5sIz0CJ5vHvDd/mgsh67g49x/0Z/8Ps0Iv8b/hqno58jB1+BzStsqJv3BNxNr8MK/6H4q/0pEbfZUFkKo9GrmWn2jhtc7KlTgGfrb+XSwLrmBV8iW9lPMvXQi/yx2uzoXwF5J5jZ/UmKCv66UoFft5rAAAKg0lEQVQVdq2EtQtgzTNwbB/0Op17Xqtl0cWPcpBefic0CU/4pzOBfzoTGBMu44vBl7lp4uvw+JVwWgFM+jyM/zT0aXrNJeMnK/opZkjeMCoryppdFxCYkhtk5tgQnx2fwch+AeojysJNYZ5Y1cArWzfiKORfbAXftM1mHcrc8Cxu/dVCDv3zCVj5R3jlO+5t6AUw/joYMx36j/A7atqzop9imk6jcBoHuChQzKXBtVweWM0AOUxYA7zjnMVvGy5gcaSQ6pE9YaR7FRw7ucZ0RHUdUPhF97a3BNa/AOtegL/PdW8Dx8Loq2DkFZB/IWTadXq7mhX9VKLKyH7CzMBbFAY2MyWwkVGBXQAc0J684ZzNkshk3nQmUk1Pn8OalBTMQJrpyz+jn/DJMRlcO7qYy/ZsJPO9h6mPKMvKI/yzLMI7OyO8Vx4hs38eu8t3+hA8fVjRT1aOAwe3Q+U6qFwDu1bBrlVsvb0X8DuqtTsrnNE803A57zrjWa/5NrbedL5IQ7MT9oWB//Nu2Q11nBfZxEWBYi4cup5vDNvOty+JAFCy/wA89x9w+mQYPMG99RjYpX9CqrOin+jCdbB/G+wvhb2b3VvVRvhwIzQcdbeRIJw2DsZew233P8a2qx5is+ZZkTcJqZYs3nYm8rYzEYBs6jhbSjk3sJmRlX9iVPlyKP7LRzv0HAQ5Z0LOWPc2YBT0PwN650LAPuNtZUXfb3VH4PBuqK6AQ+Xu7eBOOLADDu5wn6Mfbd9zsPvBn3wTDD4LBo2HnHGQ6Z409eh1vyF/ms10aJJHLVks03Esi4xjx3OPoc+ug6N73emd96xz76s2wuo/Q/3hj3YMZUPfYdA3H/rlQ5+h0CfPve99uvtlEbIzhpuyoh9vjgN11e4QyGP7vfu9cLTK/SAfroQje9zb4Up326Z6DXE/yPkXQb8RMOAMt2Uz4Azo1rfr/yZjulqPgTDyMvfWSBWqd8H+rbBvq3t/YLvbQCp/H2oPnfQye4447DqsVB5Rdh9x2HNU+fCo8uFRh6qjyt5j7m1fjXKsAQbnDk35YwoxFX0RmQ48hHth9MdV9YEm67OAPwDnAvuAz6nqdm/dt4EvARHgdlVdHLf08aQK4VqoPxp1OwJ1h71773HdYag7BLXVbsGuPQQ1B737A1B7ENRp/j0yurutj56D3Nb6yMvdAt/7dPenap888idNZWfZJmBTF/7xxiQBEXfMf59cGDH15PW11Ywf1o/zvnwfg2U/g2U/g7IPcFq3g+QOOshkOcgAqsmQSLMvX6cZ7D9yAB45H7L7QHZfyO4NWb0/us/q5d33hMye3n0v95d2Zg/I6JHwvy5aLfoiEgQeAa4CyoHlIrJQVddHbfYl4ICqjhKRG4CfAp8TkQLgBmA8cDrwDxEZo6rN/1fviLojsPwxfvbTnxCuqSY7BNkhITvo3nfLgO4ZQrcQdPPuu2cI3TOgR6Z7H4jxDMKaBuVQnXKoVjlQqxyshQM1yv5apT7Ui7vm3Ou2VLoPgG79oWcOdB94vAvmVHaWlbfpylVN2ZBLk9RaGP3TFkedSadYq/TmGAOkmgEcop8coZ8cpj+H6StHCWx+nllTxriNtyOVbrdSXbXbyIu1bAVCbvHP6ObdukNGNoS6effZ7vJQlrsslOXdst2uqUk3dujvb00sLf0pQImqlgKIyHxgJhBd9GcCP/AeLwAeFvf/3ExgvqrWAdtEpMR7vffiEz9KuA7+8QO+eS7UaQ/qyaCODGrJpF5D1JFJLZnUaibVZLLHe16jWdSQRU0kkxrNpuzV35N91Z0c0yyO0o2j3v1hunFUszlKN3dyqRDQ07tF2fHzT3P3wq/F/c8zJi20MPonVq03eoRqelCtPdjGkBMOlwHsePlZbn3pT83u2T0DemUKvbKE3lnQM1O859AjQ+iRKZw+sA9z7vwqNNS4Ay0aaqHhmPs8XOt29zbUuo/DdRCucadBCde4PQR5UxKi6OcC0ad4lgPnt7SNqoZF5BAwwFu+tMm+nXNOdvf+8J1KApndGdaRD83yeeRfeVnrG7ak0z+0xphOE8O/3wbcPux9zazb8fNPM/dvP2jXWwcFhg7dyLYvt2v3mImqnnoDkeuB6ar6Ze/5F4DzVXV21DbrvG3Kvedbcb8YfgAsVdU/ecufAF5W1QVN3mMWMMt7OpbE69AeCOz1O0QbJFPeZMoKyZU3mbJCcuVNxKz5qq1PhxtLS78C9wz9Rnnesua2KReRENAH94swln1R1XnAvBiy+EJEilS10O8csUqmvMmUFZIrbzJlheTKm0xZm4rlzIblwGgRGSEimbgHZhc22WYhcLP3+Hpgibo/IRYCN4hIloiMAEYD78cnujHGmLZqtaXv9dHPBhbjDtl8UlWLReQ+oEhVFwJPAH/0DtTux/1iwNvuWdyDvmHgq50ycscYY0xMYhqnr6qLgEVNlt0b9bgW+EwL+/4I+FEHMiaChO16akEy5U2mrJBceZMpKyRX3mTKeoJWD+QaY4xJHTZbkTHGpBEr+m0gIl8TkY0iUiwiD/qdJxYi8nURURFJ2PlpReRn3n/XNSLygogk3ARDIjJdRDaJSImIzPU7z6mIyFAReV1E1nuf1Tv8ztQaEQmKyCoRaf9JLl1ERPqKyALvM7tBRC70O1NbWNGPkYhcgXuG8dmqOh74uc+RWiUiQ4GrgUSfQepV4CxVnQhsBr7tc54TRE1Fcg1QANzoTTGSqMLA11W1ALgA+GqC5wW4A9jgd4gYPQT8XVXPBM4meXIDVvTb4v8BD3hTSqCqH/qcJxa/BL7FSSebJxZVfUVVw97TpbjncySS41ORqGo90DgVSUJS1d2qutJ7fBi3KCXs1clFJA/4JPC431laIyJ9gKm4IxZR1XpVPehvqraxoh+7McClIrJMRN4UkfP8DnQqIjITqFDVD/zO0kZfBF72O0QTzU1FkrBFNJqIDAcmA8v8TXJKv8JtnLQwPW1CGQFUAb/3uqMeF5GkutCvzacfRUT+AQxuZtV3cP9b9cf9uXwe8KyIjFQfhz+1kvce3K6dhHCqrKr6f94238HtmniqK7OlKhHpCTwP3KmqzVy4wX8ici3woaquEJHL/c4TgxBwDvA1VV0mIg8Bc4Hv+Rsrdlb0o6jqtJbWicj/A/7iFfn3RcTBnX+jqqvyNdVSXhGZgNsi+cCbpjYPWCkiU1S1sgsjHneq/7YAInILcC3wMT+/SFsQ03QiiUREMnAL/lOq+pfWtvfRxcAMEfkEkA30FpE/qepNPudqSTlQrqqNv5wW4Bb9pGHdO7F7EbgCQETGAJkk3oRLAKjqWlU9TVWHq+pw3A/qOX4V/NZ4F+n5FjBDVY/5nacZsUxFkjC8ac2fADao6i/8znMqqvptVc3zPqc34E7hkqgFH+/fUJmIjPUWfYwTp5lPeNbSj92TwJPejKL1wM0J2CJNVg8DWcCr3i+Tpap6m7+RPtLSVCQ+xzqVi4EvAGtFZLW37B7vzHrTcV8DnvIaAKXAf/icp03sjFxjjEkj1r1jjDFpxIq+McakESv6xhiTRqzoG2NMGrGib4wxacSKvjHGpBEr+sYYk0as6BtjTBr5/9mG+MmolgKiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\" df = degree of freedom\"\"\"\n",
"df=2\n",
"X=stats.t.rvs(df=df,size=1000)\n",
"hist_trunc(X,-7,7,20)\n",
"x=np.linspace(-7,7,100)\n",
"plt.plot(x,stats.t.pdf(x,df=df));\n"
]
},
{