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Lab_11_hypotesis_testing_part_IV.ipynb
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{ | |
"nbformat": 4, | |
"nbformat_minor": 0, | |
"metadata": { | |
"colab": { | |
"name": "Lab_11_hypotesis_testing_part_IV.ipynb", | |
"provenance": [], | |
"authorship_tag": "ABX9TyNURtrcF+uvn5MyvXEyc0cP", | |
"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/gist/jamm1985/672a23052f654121163e51cada769112/lab_11_hypotesis_testing_part_iv.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"Видео лабораторной: https://youtu.be/wAykF0_WGVg\n", | |
"\n", | |
"TG: https://t.me/data_science_news\n", | |
"\n", | |
"\n", | |
"\n", | |
"---\n" | |
], | |
"metadata": { | |
"id": "AOdqg07rkzKl" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "BEaMsDiLIJvO" | |
}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pylab as plt\n", | |
"\n", | |
"from scipy.stats import norm\n", | |
"from statsmodels.distributions.empirical_distribution import ECDF\n", | |
"\n", | |
"plt.rcParams['figure.figsize'] = [12, 8]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"# KS Gondess-of-fit test\n", | |
"\n", | |
"Пусть $X_1,...,X_n$ i.i.d. выборка из некоторого распределения $F_1$ _(CDF)_.\n", | |
"\n", | |
"Тогда выборочная функция распределения _(ECDF [лабораторная №7](https://youtu.be/dXR2V-_F3yg))_ $\\hat{F_1}_n = \\frac{\\sum_{i=1}^nI(X \\leq x_i)}{n}$ \n", | |
"\n", | |
"Пусть $Y_1,...,Y_n$ i.i.d. **(независимая от $X$)** выборка из некоторого распределения $F_2$ _(CDF)_. С аналогично заданной эмпирической функцией $\\hat{F_2}_n$\n", | |
"\n", | |
"Предположим, мы хотим протестировать принадлежат ли реализации $X_i$ и $Y_i$ к одному распределению. Для этого сформулируем тест:\n", | |
"\n", | |
"$H_0: \\hat{F_1}_n = \\hat{F_2}_n$ VS $H_1:\\ \\hat{F_1}_n \\neq \\hat{F_2}_n$\n", | |
"\n", | |
"Непараметрическая тест статистика Колмогорова-Смирнова для двух выборок имеет вид: $D_n=\\mathrm{sup}|\\hat{F_1}_n(x) - \\hat{F_2}_n(y)|$\n", | |
"\n", | |
"Или для одной выборки и известного распределения $F$: $D_n=\\mathrm{sup}|\\hat{F_1}_n(x) - F|$\n", | |
"\n", | |
"Где тест-статистика $D_n$ подчиняется [распределнию Колмогорова-Смирнова](https://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test#Kolmogorov_distribution)\n", | |
"\n", | |
" " | |
], | |
"metadata": { | |
"id": "99OjgeeOXm8S" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"\n", | |
"\n", | |
"[Source - wikipedia](https://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test#/media/File:KS_Example.png)" | |
], | |
"metadata": { | |
"id": "fV9R_DYUfqPX" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## KS one-smaple test EXAMPLE" | |
], | |
"metadata": { | |
"id": "urJxWD09gBVq" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"### Выборка №1 (sample_1)\n", | |
"\n", | |
"$X_1, X_2, ... , X_n$ $\\sim$ $N(\\mu, \\sigma^2)$, \n", | |
"\n", | |
"где \n", | |
"\n", | |
"$n=100$, $\\mu=5$, $\\sigma^2=4$" | |
], | |
"metadata": { | |
"id": "RzescbssgRv1" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"mu=5\n", | |
"sigma=2\n", | |
"rv_norm = norm(mu, sigma)\n", | |
"sample_1 = rv_norm.rvs(100)\n", | |
"sample_1" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "NlYa7omCXliO", | |
"outputId": "f801935a-7d4b-41d9-f7d5-77aaaf35c043" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"array([ 5.07919062, 3.69536054, 4.53606321, 6.24957629, 6.20681993,\n", | |
" 4.3325407 , 6.71075116, 3.85535992, 6.24678873, 3.32511597,\n", | |
" 5.48017657, 9.57105043, 2.74295381, 6.32608559, 6.73466131,\n", | |
" 3.04849212, 8.63592328, 4.2217072 , 6.24527705, 3.84945906,\n", | |
" 5.2809855 , 4.23543496, 6.57530968, 9.40377223, 6.34311573,\n", | |
" 6.47293858, 6.05306387, 4.50916074, 2.17605635, 2.32171392,\n", | |
" 7.16908996, 3.43958813, 9.04263607, 6.2556673 , -0.47138654,\n", | |
" 6.35835368, 2.96462229, 6.33263509, 8.01704533, 4.43518798,\n", | |
" 4.76170265, 7.01271561, 4.40674149, 6.13967201, 1.24710988,\n", | |
" 5.05940738, 5.85418212, 5.18729145, 7.11459916, 4.54973349,\n", | |
" 3.65892012, 3.96966245, 5.83832702, 1.81565688, 5.19720084,\n", | |
" 3.39615097, 8.84907862, 4.79663819, 6.38488336, 5.06727338,\n", | |
" 4.05807249, 4.98007024, 6.14216103, 5.28447523, 9.47445364,\n", | |
" 5.16603127, 4.05867209, 8.11540761, 2.44188567, 2.57328732,\n", | |
" 5.50259682, 4.29106629, 3.27483081, 4.86030226, 5.58773211,\n", | |
" 4.19988315, 3.49320536, 3.67345651, 1.7852449 , 4.18945262,\n", | |
" 7.45539349, 7.09533592, 7.85784015, 4.58848033, 3.83023784,\n", | |
" 3.32461689, 5.7090373 , 4.50230445, 6.46803219, 5.08025297,\n", | |
" 1.76354549, 5.98467082, 4.3915565 , 7.42838796, 4.33357601,\n", | |
" 5.78448608, 1.91651038, 4.1241221 , 6.11330295, 3.62654898])" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 16 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"ecdf = ECDF(sample_1)" | |
], | |
"metadata": { | |
"id": "T-zTV_I6IXXX" | |
}, | |
"execution_count": null, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html\n", | |
"from scipy.stats import kstest " | |
], | |
"metadata": { | |
"id": "1INRA2fdhXE4" | |
}, | |
"execution_count": null, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"Alternative: $\\hat{F}_1 \\neq F$ - двусторонний тест" | |
], | |
"metadata": { | |
"id": "S0VFAz5jjJuD" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"y_ecdf = ecdf(sample_1)\n", | |
"plt.plot(np.sort(sample_1), np.sort(y_ecdf), label='ECDF')\n", | |
"plt.plot(np.sort(sample_1), rv_norm.cdf(np.sort(sample_1)), label='True CDF')\n", | |
"plt.legend(fontsize=15)\n", | |
"plt.xlabel('Normal RV sample (N=100)', fontsize = 15)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 520 | |
}, | |
"id": "a0PKb7LAhCg3", | |
"outputId": "305dc309-87f7-4ad8-e728-121b97cab345" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, 'Normal RV sample (N=100)')" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 19 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"# Test the same distribution\n", | |
"kstest(sample_1, rv_norm.cdf, N=100)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "Ku1p0_p3ism_", | |
"outputId": "6ceca334-6b40-45c3-abfa-73284e3329dd" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"KstestResult(statistic=0.06418295118648226, pvalue=0.8045492039789772)" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 20 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"y_ecdf = ecdf(sample_1)\n", | |
"plt.plot(np.sort(sample_1), np.sort(y_ecdf), label='ECDF')\n", | |
"plt.plot(np.sort(sample_1), norm(5,4).cdf(np.sort(sample_1)), label='Norm(5,4) CDF')\n", | |
"plt.legend(fontsize=15)\n", | |
"plt.xlabel('Normal RV sample (N=100)', fontsize = 15)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 520 | |
}, | |
"id": "9cKpVUtXkxjI", | |
"outputId": "66fcd435-1f07-4acb-dbd6-5dc6ab7f75e2" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, 'Normal RV sample (N=100)')" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 21 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"# Test another normal\n", | |
"kstest(sample_1, norm(5,4).cdf, N=100)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "GkLouv3Vj2Cz", | |
"outputId": "8cbe6f59-93c2-419a-f7c2-3baf7687d0dc" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"KstestResult(statistic=0.20312792483611797, pvalue=0.0004287358601834932)" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 22 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"# Test another sample from the same distribution\n", | |
"sample_2 = norm(mu, sigma).rvs(100)\n", | |
"\n", | |
"y_ecdf_1 = ecdf(sample_1)\n", | |
"y_ecdf_2 = ecdf(sample_2)\n", | |
"plt.plot(np.sort(sample_1), np.sort(y_ecdf_1), label='ECDF Sample 1')\n", | |
"plt.plot(np.sort(sample_2), np.sort(y_ecdf_2), label='ECDF Sample 2')\n", | |
"plt.legend(fontsize=15)\n", | |
"plt.xlabel('Normal RV sample (N=100)', fontsize = 15)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 520 | |
}, | |
"id": "7ssCyP_LkYfR", | |
"outputId": "4157fcd1-fbd6-4925-f07c-da8b9a01895e" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, 'Normal RV sample (N=100)')" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 23 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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NRuPGjbn66qt55plnOH78eKXrV3XtFStWVJm5tLSUSZMmER8fj6+vLyEhISQmJvLyyy/X3BemhiQlJXH77bdf9nkWL17M0KFDadmyJb6+vsTHx/PPf/4Tu91eAylFRKTByToEyf+B2cMxX42CD35N2cp/sfYETCz9LbfxOq/FfUHYXVN4aeyzPHP7NXRtGawS7IQ0IlzLAgMDWbhwYaXtMTExFR/v2rWL3r1706hRIx577DHi4uLIyclhwYIFDB8+nDZt2tCpU6dK58vOzmbDhg1MnjyZKVOmsHDhQrp27XrWdUaPHl2pLLZv377KvA8++CAzZszgmWeeITExkaysLFavXs38+fN58sknL/nr4MymTJlCQUEBf/3rX4mMjGTFihWMHj2a/fv388Ybb1gdT0RErFZaBIdWQcoS2LMIMnYBkOkWxrel1/BdWUd2+VxFz/go+sc35bFWTfBw01hjfaAiXMvc3d3p3r37eY8ZPnw4wcHBrFq1ioCAgIrtAwcOZOTIkQQFBVV5vhtvvJGRI0fSq1cvhg0bxs6dO3Fzc6vYHxUVdcHr/6ygoID333+fCRMmMGbMmIrtt956K6ZpVusc9dHbb79NSEhIxfOkpCQKCgr429/+xksvvYSXl5eF6URExBIn98GexZCyGPPADxilBdgND3Z4dmBe2e/4zt6RooDW3Nj5Cv4Q35SuLRvjphtZ1Dv654rFli9fzvr165k4ceJZJfhnHTt2pEWLFuc9R1BQEK+++iopKSksWrTokrPk5+dTWlpK06ZNK+0789c5+fn5PPjgg7Rt2xZfX1+io6MZNWoUOTk5lV7zt7/9jdGjR9OkSRNCQkJ4/fXXAfjggw9o1aoVQUFB3HfffRQVFVW8btq0aRiGwbp16+jZsyc+Pj7ExsYyd+7cC34O27ZtY8CAAfj7++Pv78+QIUPOOW3kTGeW4J916dKFoqIiTp48ecFriohI/VdUkMvRdV9yZMaD5LzaAd7qAl+P4ejeLcws6cm9JWOIL3yHhz2ex/3aB5n05ztY8eT1PDcwjm7RwSrB9ZRGhOtAWVlZpW3u7uVf+mXLluHm5kbfvn0v6xpJSUm4u7uzevVq+vfvX7Hd4XCcdX3DMM4aMT5TaGgokZGRjBs3jkaNGtGvXz/8/f0rHVdQUIDdbmfChAmEhoZy+PBhJkyYwJAhQ/jmm2/OOvaNN95gwIABzJo1i//+97+MGTOGtLQ01q1bx1tvvcWhQ4d49NFHiY2NrTT1YujQofz5z3/m6aefZurUqQwZMoT169dXTBP5pZSUFHr06EFCQgLTp0+nrKyMZ599loEDB7J27dqLmpv1448/EhQURFhYWLVfIyIizss0TdJzizl0sqD8kZlP0fGdhKetoF3eGro4dtDMKKXQ9ORHRxyrjOtJCeiOW0gMkcG+9Az25YmYJrQN99dc3wZERbiWZWZm4uHhUWn7/v37iYqKIjU1ldDQUHx8fC7rOt7e3oSEhHDixImztj/yyCM88sgjFc979Ohx3jfLTZs2jWHDhnHbbbdhs9no0qULw4YN4+GHH8bT0xMoL8yTJ0+ueE1ZWRnR0dFce+21HDp06KwR7DZt2vDOO+8A0LdvX+bMmcO7777LwYMHK0bAly5dyty5cysV4fvvv5/HHnsMKJ8CEhcXx8SJE5k9e/Y5s7/wwgs0bdqUr7/+uiJrx44dufLKK1mwYAEDBgw4/xfxtB07djB58mSeeOKJKv/RICIizqegpIzDJwsryu7hn0vvyQKOnCrAVlrAr2zbSbJt4ja3LUQa6QCc8GzBjpDbKWjZG5+YnsSHBdPbz0uF1wXUryL89ZNwfKs1127aAW66+JUTAgMDWbx4caXtzZr9b/HsmvqDdq55vGPGjOGOO+6oeH6uEd4zXX/99ezdu5cFCxawePFiFi9ezJgxY/jiiy9Yvnw5Nlv5bJqPPvqISZMmsWfPHvLz8ytev3v37rOKcJ8+fSo+ttlsREdH4+vre9Y0kJiYGFatWlUpy+DBg8967aBBg5gzZ06V2RcvXsw999yDzWarGAWPjo4mKiqK5OTkahXhU6dOcdttt9GxY0eefvrpCx4vIiJ1Ky2niH0Z+ZWK7uGThWTkFZ91bCNPGz2DMhjpvoWrgtbTIm8zbmYZDndfzOjrILYfxPQhvHEU4RZ9PmKt+lWE6yF3d3cSEhKq3B8REUF6ejpFRUV4e3tf8nWKiorIzMwkPPzsP8otWrQ47/XPxd/fn6FDhzJ06FBM0+T5559n/PjxzJ8/n0GDBjF37lzuvvtuRo4cyUsvvURwcDDHjh1j8ODBZ831Bc56ox+Ap6fnObf98nVApWkJYWFhHDt2rMrcGRkZvPLKK7zyyiuV9h0+fPiCn3dRURGDBg2iuLiYefPmVYwqi4iI9QpL7Ez8+ic+/PFgxTabAc2CfGgR7EvfdmFEBvvSqlEx7Qo3cEX6SjwPLsPIOVp+cFgcdPgzxPTF1uIacNfPeKlvRfgSRmSdXVJSEs899xxLliyp9q/uz+X777+nrKyMa665pgbTlY9WjxkzhvHjx7Nz586KUdnExETefvvtiuOWLVtWo9cFSEtLo0mTJmc9v+KKK6o8Pjg4mMGDB3P//fdX2neuN8SdyW63c+edd7Jjxw5WrlxZ6R8UIiJina1Hsnnk443sS89nxK+i6NMujBbBvjQL8sEDB6QmQ8r88uXNUjcAJngHQqskaN0HYvpCYITFn4U4o/pVhBugnj170rVrV55++ml69epVaerC1q1bCQoKIjIysspzZGVl8cQTTxATE3NZb7orLS0lPz+/0ojtnj17ACrKYWFhYaUlxWbMmHHJ163K3LlzadeuHVD+pr8vv/ySbt26VXl8nz592L59O127dr3o6SZ//vOfWbhwIYsXL6Zt27aXlVtERGqG3WEyeWkKf1+8hxA/L2bcn0iPmJDyG1qk/Bf2LoF9y6E4GwwbRHSF656AmD7Q7CpwU82R89N3SC0rKytj9erVlbZHRkYSEVH+r9MZM2bQu3dvEhISePTRRytuqPHNN9/w7rvvsmbNmooifOb5cnNzWb9+PZMnT6agoICFCxde1pu7srOziY2N5Z577qF3794EBgaya9cuJk6cSERERMWc3X79+jFq1CgmTJhAYmIiCxYsYMmSJZd83apMnToVT09P4uPjmTp1KikpKcyaNavK48eNG0e3bt0YMGAA9913HyEhIaSmprJo0SJGjBhBUlLSOV/30ksvMWXKFJ566ilsNttZ/7/i4uLOuaydiIjUrsMnC3j0400kHzzF4A5N+GunUzTa8zp8vRgyywdoCIiAuN+UF9/o68A32NrQUu+oCNey7Ozsc05XGD9+PGPHjgWgbdu2bNiwgYkTJ/Lqq6+SmpqKr68v3bp1Y+bMmWctF/bz+QzDICAggJiYGO666y4eeuihc67/ezECAgJ4/PHHWbBgATNnziQnJ4eIiAhuvPFGxo4dS2BgIAB//OMf2bdvH2+++SZFRUX069ePmTNnVvvGHdU1e/ZsHn30UcaOHUtkZCQff/wxXbp0qfL42NhYVq9ezdixY3nggQcoLCwkIiKCPn36nHUnv1/69ttvAZg4cSITJ048a9/3339fZYEWEZGaty01m/dXHmD+5qN4edj49y0R9F93P3y6B9y9oWUPSLi3fMpDaFvQyg5yGQyr7hiWkJBgJicnV7n/p59+qvi1uLiWadOmce+995Kbm4ufn5/Vcaqk71ERkZpRZnewaMcJ3l95gLUHTuLr6cZtVzVn1NUBNJ17G2SnwuDJ0OYG8Li85UbFNRmGsd40zUqrB2hEWERERCyRVVDC7HWH+ejHg6RmFdK8sQ9jB7RjSEIkgfYs+ODXkH0Ehn8KUT2sjisNkIqwiIiI1BnTNNl5PJcPfzzI3I1HKCp10L1VMM8NjKNvu/DyWxXnZ8KHg+DUQRg+RyVYao2KsDidESNGMGLECKtjiIjIZTBNk/S8YnYfz2PXiVz2nMg9/d888orL8HK3cUvnCEb0iKLdFQHgcMDhH2HzLNj+JdiL4c6PIbqn1Z+KNGAqwiIiInJZsgpK2H2ivPDuPp7L7hPlj1MFpRXHNPb1oG1Tf267KoK2TQPoH9+U4EaekJEC370FWz4uXxbNo1H5ShCJf4RmVb9BWqQmqAiLiIhIteQXl7EnLY/dx8tHd3efyGXX8VzScv93a2M/L3diw/3oH9+U2HB/2ob70ybcnxA/z/+t8V5wErZ9AJtnl98Mw7CV3/yi91ho92vwbGTJ5yeux6mLsGmaF31jBJG6YNVqKyIidcE0TXYeTOVg6lH2Z+SzPz2fvel5HM8uqjjG091GVEgjBrZsRKvQAKJD/Wgd0ogwf69f/N1dAPYCyDLh2Obykd/d34CjFMLjod946DAEAqq+c6hIbXHaIuzh4UFhYSG+vr5WRxGppLCwEA8PD6tjiIjUire/3cadq/rTzsg7e4f3Lw7MOv1IuYiT+4WXT3voNAyadri8oCKXyWmLcFhYGKmpqURERODj46ORYXEKpmlSWFhIampqxS2nRUQakpIyBwfWfEFjI4/MhEcJbNoad7ca+js4IAKieurWx+I0nPY78efb2h49epTS0tILHC1Sdzw8PAgPD9etl0WkQVr80wl6lq6kxDeYJjeNVWmVBs2pv7sDAgJUNkREROrQZ2tS+IfbRtzbD1MJlgZP3+EiIiIuLLuglB/3ZbAiJYMVezKIPbUMX88iaD/I6mgitU5FWERExIUUldrZcPAUK1IyWJmSwZbUbEwTfD3d6N6qCU/478LMbowRpRtZSMOnIiwiItKAORwmO47lVBTftftPUlzmwN1m0KVFEA9f34Zr24TQOTIID0cJvPYDtL8F3LQyjjR8KsIiIiINzJFTBSzflc7OndvYeDCT7KIyAFo1acSDnRuT0DKEjpFBNPJ0O/2KLMjOgoOroCQX4m6xLrxIHVIRFhERaUB+2JPOve+v4wXbVF50X1K+0ev0zjxg2+lHVbyDILpX7YYUcRIqwiIiIg3E4ZMFPDRrI7c23sfw/CWYsTditL/14k4SeiW4e9ZOQBEnoyIsIiLSABSW2PnjR+txcxQzweM9aByFMeQD8PCxOpqI01IRFhERqedM0+SZz7eQf3wPn3fagcfOffC7uSrBIhegIiwiIlLPLdudzjXbnmOS13LYCXS4A1pfb3UsEaenIiwiIlLP7V/7Ffe6L8feaThubfpC25usjiRSL6gIi4iI1GelRfTd9yon3JsR/utJ4OFtdSKResNmdQARERG5dKcWvUakeZQtnZ5VCRa5SCrCIiIi9VTBsd34rXuT/9q7E/urQVbHEal3VIRFRETqoaOnCvjpvQcocriTl/QiLZs0sjqSSL2jIiwiIlLPbDh0irf+8RpdyzZyrOtohvVJtDqSSL2kN8uJiIjUEw6HyRebUhn/+RoWebxPUUg8sQMetTqWSL2lIiwiIuKkHA6TncdzWbM/kzX7TrJmfybtijbype9MmpRlYdzyGbjpr3KRS6U/PSIiIk7C7jD56VgOa/afZPW+TNYdOElWQSkAiQGn+Mh3JvGOlZiNWmDcNBOad7U4sUj9piIsIiJiEbvDZMfRHFbvyywf9d1/ktyiMgBaBPvSr10410Z6cn3aB/hvmgp4QZ/nMbr/WUulidQAFWEREZE6tC01m5UpGazZf5J1+0/iXZxOgFFARJA3I9oE0SkykI7Ngwjz94aDq+C7v0JBJnQZDtc/C/5Nrf4URBoMFWEREZE68u324zzw0XoAWof4MKnpt/Q98R8MHFAI7Dn9OFOLa6D/p9CsS13HFWnwVIRFRETqyCfJh2ka4M38+9oSuuhh2LsE4m+HK28+9wt8QyC6FxhG3QYVcREqwiIiInUgq6CEZbvTGdshm9AZD5ZPd/j136HrCBVdEYuoCIuIiNSBhVuPcQ//5e5dsyGoBdy/CK7oZHUsEZemIiwiIlKLcotKmbZiP6ErnmGsx7eYV/4GBv0TvAOtjibi8lSERUREakF+cRkf/HiAKcv28pfSqQxz/5ZTXf5M49+8pKkQIk5CRVhERKQGFZbYmb76IP9etpfM/GKmhH7KDbnfwjUP0viGv6oEizgRFWEREZEaUDl+LbUAACAASURBVFRqZ+aaQ7y9dC8ZecX0jGnC60HfEL5tLiSOBJVgEaejIiwiInKZNhw6xWNzNrMvPZ9ftW7C5OFduDrlLVj5Llz9B+g/USVYxAmpCIuIiFyiolI7f1+8hynL93JFoA8f3NeN69qElN8NbuXfIeE+uPk1lWARJ6UiLCIicgk2H87isTmb2ZOWx7CrI3lmQDv8vT1g6cvww+tw1d1w8xsqwSJOTEVYRETkIpSUOXhryR4mL9tLqJ8X0+69mqS2YeU7l70GSydC5+Hw6zfBZrM2rIicl4qwiIjIRfjwxwP88/sUbruqOc8NjCPQx6N8xw+T4Pu/Qsdh8Jt/qASL1AMqwiIiIhfhQGY+jX09eOOOM+4Kt/ItWPICdBgCt7wNNjfrAopItemfqyIiIhchq6CUIF/P/2348W1Y9Cy0vxVu+bdKsEg9oiIsIiJyEbILS/83HWLNFPjmKYgbBLe+C276RatIfaIiLCIiUk1r9mWy6XAW4QFesG4qfD0Grvw13PaeSrBIPVStImwYRn/DMHYZhpFiGMaT59jfwjCM7w3D2GgYxhbDMG6u+agiIiLW+XjdIe56bw2hfl5MiFwPX42G2Jvg9vfBzcPqeCJyCS5YhA3DcAP+BdwExAG/NQwj7heHjQU+MU2zCzAMeLumg4qIiFihzO7gxfk7eOKzrXRv1YT/XnuAkKWPQ5sb4I4PwN3zwicREadUnd/jdANSTNPcB2AYxmxgELDjjGNMIOD0x4HA0ZoMKSIiYoXswlKe/WgRe/fv46nOzbg/ahNuC5+A1n3gjo/A3cvqiCJyGapThCOAw2c8PwIk/uKYccC3hmE8BDQC+tZIOhEREQu98MUm/pr6ewK8CmAn5Y9WSTBsBnh4WxtORC5bTc3s/y0wzTTNNwzDuAb4yDCMeNM0HWceZBjGA8ADAC1atKihS4uIiNS8rIISdm/bQIBHAfT4C0QmgpsnRPfUSLBIA1GdIpwKRJ7xvPnpbWf6PdAfwDTNHw3D8AZCgLQzDzJNcwowBSAhIcG8xMwiIiK17ouNqcSWzwqETr+FsCutDSQiNa46q0asA9oYhhFtGIYn5W+Gm/eLYw4BfQAMw2gHeAPpNRlURESkLn2SfIReAcfA3QdC2lgdR0RqwQWLsGmaZcCDwDfAT5SvDrHdMIwXDcP4zenDRgN/MAxjMzALGGGapkZ8RUSkXkpJy2PHsRx+5XUAwtvrbnEiDVS15gibprkAWPCLbc+d8fEOoEfNRhMREbFG8oGThHGK0OwtcNXTVscRkVqiO8uJiIj8wsZDWQz2WY+BWX77ZBFpkFSERUREfmHDoVMM9kyG0CshtK3VcUSklqgIi4iInCG/uIys9CO0Ld4KcbdYHUdEapGKsIiIyBn2pedzo22dpkWIuAAVYRERkTPsy8jjJttaSoJaQ1g7q+OISC1SERYRETnD0aNH6G7bga39LWAYVscRkVpUU7dYFhERaRAaH/wGN8OEDoOtjiIitUwjwiIiImeIy/qeY27NIDze6igiUstUhEVERH5WcJL2xZvYEnCdpkWIuAAVYRERkZ/t/Ao3HOwP62d1EhGpA5ojLCIictqJNR9T7AjFrVlnq6OISB3QiLCIiAgwf/V2go+vYqP/ddzZvaXVcUSkDqgIi4iIy/tk3WGWzv8QD8POjUMeoJGXfmEq4gr0J11ERFzajDUHeWbuNuYGbcT0bI53y25WRxKROqIRYRERcVnpucU8+8U2bmrjS+fSjRi6iYaIS1ERFhERl3UsuxCHCaOa7cGwl0DcIKsjiUgdUhEWERGXlZFXDEDzY9+CfzOISLA4kYjUJRVhERFxWRm5JTSikMDU5eWjwTb9tSjiSvQnXkREXFZmfgl9bBsx7MWaFiHiglSERUTEZRWWlHGT2xpMv6YQmWh1HBGpYyrCIiLissqKcult24TRbqCmRYi4IP2pFxERlxWZuRJvoxTa32J1FBGxgIqwiIi4rKjsdeTgBy2usTqKiFhARVhERFyWh72AHMMfbG5WRxERC6gIi4iIyzIcpdgNd6tjiIhFVIRFRMRl2cwy7IZGg0VclYqwiIi4JLvdTlDREUpsvlZHERGLqAiLiIhLWjfvHaIdhyjsNMLqKCJiERVhERFxOfn5ebTc/AZ73WPofPP9VscREYuoCIuIiMtZ/8krXEEG9j4vYmjFCBGXpSIsIiIuZWVKBtEHZvGTb1dirxlgdRwRsZCKsIiIuIwNh07xhw+TCTOyiY7XTTREXJ2KsIiIuISfjuUw4j9rifADL0rw9m9idSQRsZiKsIiINHj7M/L53XtraeTlzgfD2pRv9AmyNpSIWE5FWEREGrzXv91FcZmdj36fSLPcLeUb/ZpaG0pELKciLCIiDd6p/BLahvsTE2CHr5+E8A7Qpp/VsUTEYrrBuoiINHhFpXZ8Pd1h8TjIT4PfzgI3D6tjiYjFNCIsIiINXlGpg3j7dkj+DySOhIirrI4kIk5AI8IiItKg2R0mp3JyuTf/bxDYAno/bXUkEXESKsIiItKgLd+TztDiOYS7H4Ihn4GXn9WRRMRJaGqEiIg0aD+s/IFR7vOwt78d2vS1Oo6IOBEVYRERabBO5hUx4MDLlLr54nbTy1bHEREnoyIsIiINkmmaTJ8zh6623eT0eBr8Qq2OJCJORkVYREQapEmLdrNxz0EAmsZ2sziNiDgjFWEREWlwZq89xD++S6FPTED5BncvawOJiFNSERYRkQZl6a40nvliG73bBHNn8O7yjR4+1oYSEaek5dNERKTBWL0vk5HTN9AjtIip5vPYNq0BwwY+ja2OJiJOSEVYREQahDX7Mrn3/XXc5reNF4v/ia2wFH7zD2jZA3yDrY4nIk5IRVhEROq9tftP8sC0H3nR5xOGFH4JTTvAkA+gSWuro4mIE1MRFhGRem31vkyenfYVs93fol3JHrj6D3DDX8HD2+poIuLkVIRFRKReOpRZwKRFuyja+gVzPd7F18MNBn0IcYOsjiYi9YSKsIiI1CtpOUW89d0ePl+7j6fdZ3CXxzeUNe2C7Y73ITja6ngiUo+oCIuISL2QXVDK5GV7mbZqPxH2YywKnExE4W7o/mfc+74A7p5WRxSRekZFWEREnFqp3cGU5ft4Z9lecovLeD56F3env4HNdIdhs+DKm62OKCL1lG6oISIiTu2T5MO89s0uro4K5ocB2Yw4+gK28Dj40w8qwSJyWTQiLCIiTu3HvZk0C/TmvX5u8P7/QWQi3D1Pq0KIyGXTiLCIiDgt0zRJPnCK6yPsMOu30CgUhs5QCRaRGqERYRERcVqpWYVk52TxaPprUJIHv/8W/EKtjiUiDYSKsIiIOK33ftjLJI/JBOfuhDs/hvD2VkcSkQZERVhERJzSvM1HCV77Oje5r4MbJkDsjVZHEpEGRnOERUTE6ew+kcuKz/7FQ+5f4OhyN1wzyupIItIAaURYREScSk5RKW9Nm84k278paf4rPAe8AYZhdSwRaYBUhEVExGlk5hXz5Hv/5eWCl3AENMf7zhm6Y5yI1BoVYRERcQpHThXwx6lLmZT3PAGeJh53zwHfYKtjiUgDpiIsIiKW230il3umruLl0teItR3FGPYZhMZaHUtEGjgVYRERsVTyroN8OGs6jxsbuI4NcPMb0Lq31bFExAWoCIuIiCXScop47ZtdNN/8d95y/xxMoNsf4er7rY4mIi5CRVhEROpUUamdqT/s4+2leym1O/jkijIcBSHY7l0AIZoOISJ1R0VYRETqhGmazN9yjFe+3klqViE3tg/nqZvaEbV4BpwMg9C2VkcUERejIiwiIrVuy5Esxs3bzoZDWbRv6seUgSbtGx+FtKNwch/4NLY6ooi4IBVhERGpVdNXH2TcvO2E+LoxO/EgiUc/wFi08+yDOv3WmnAi4tKqVYQNw+gPvAm4AVNN03z5HMfcAYyj/O0Om03TvLMGc4qISD1TUubg+Xnb+XxtCs8228Dv7F9i23wQwuLg1nfL//uzJjHWBRURl3XBImwYhhvwL6AfcARYZxjGPNM0d5xxTBvgKaCHaZqnDMMIq63AIiLi/NJyi/i/D1fS7uinrPf/Br+TmRCRADe/Am1uBJvN6ogiItUaEe4GpJimuQ/AMIzZwCBgxxnH/AH4l2mapwBM00yr6aAiIlI/bN93hB+nv8A/7V8R5JEPza+DnqMhuhcYhtXxREQqVKcIRwCHz3h+BEj8xTGxAIZhrKR8+sQ40zQX/vJEhmE8ADwA0KJFi0vJKyIiTsw0TbbMepb7HZ+TE9UP+j4BkVdbHUtE5Jxq6s1y7kAbIAloDiw3DKODaZpZZx5kmuYUYApAQkKCWUPXFhERJ7HzeC6diteT0TiekHs/tTqOiMh5VWeSVioQecbz5qe3nekIMM80zVLTNPcDuykvxiIi4kKWbthBnO0g3h0GWR1FROSCqlOE1wFtDMOINgzDExgGzPvFMV9QPhqMYRghlE+V2FeDOUVExMkVldop2foFAH7t+licRkTkwi44NcI0zTLDMB4EvqF8/u9/TNPcbhjGi0CyaZrzTu+7wTCMHYAdGGOaZmZtBhcREevZHSar9mbw5aajpG/7nrf4gELvEHyu6Gx1NBGRCzJM05qpugkJCWZycrIl1xYRkUtnmiabj2Tz5aZU5m8+RkZeEb/3+o6njWkU+7fA566ZGOFxFz6RiEgdMQxjvWmaCb/crjvLiYhItaSk5TFvUypfbj7KwcwCPN1s3BAbxBPmTCIPfAax/fG9dQp4B1odVUSkWlSERUSkSgUlZUxffZBtyctxZOzFMOD2cH8SftWYThGB+G54DVLXQ6/HIekp3ShDROoVFWEREanSnOQjzPt6AfO8nsXmeXoq3cnTjw2Apx8MnQ7tBlqYUkTk0qgIi4hIlU7lF/O8x4cY3gEw/DPwDjj7AL8w8GlsTTgRkcukIiwiIlWKOraAq2274YZ/6A5xItLgaDKXiIicW0k+vQ//ix20gs53WZ1GRKTGqQiLiMg5HZ43gcDSdD4IHKk3wYlIg6SfbCIichbTNPl08QrCtk7hO4/rGHW3RoNFpGFSERYRkQolZQ6e+nwrvsteAJsbiQ/8gxZNfK2OJSJSK/RmORERAeBUfgl//Gg9bod+4GbPtTiuewav0JZWxxIRqTUqwiIiAsD7qw6w8WA6yaFzwNYCW4+HrI4kIlKrVIRFRASAlLRcRgWsIDBnN9zxIXj4WB1JRKRWaY6wiIgAkJF2gvtLZ0JUT2j3G6vjiIjUOo0Ii4gIpmkyKGsavkY+9H8ZDMPqSCIitU4jwiIiwv4TJ7mdJexrPgiaxlsdR0SkTqgIi4gIG9evwcsoo3GHG62OIiJSZ1SERUSEY7vXAdCkVVeLk4iI1B0VYRERF5eZV4xP5k+U2bwguJXVcURE6oyKsIiICzuaVci909Zxpe0QpU3agpveQy0irkM/8UREXNSafZmMmrmBolI7V3un4tl8oNWRRETqlEaERURcjGmafPjjAYZPXUOAtwfzR7TGsyQLmnawOpqISJ3SiLCIiAuxO0ye+mwzpzZ+yVNXuHFnYgt8Ur4v3xmuZdNExLWoCIuIuJC1+0/y04YfmO81CTKBBad3ePhq/WARcTkqwiIiLqSgpIyutt3lT+7/DhqFlH/sHVj+EBFxISrCIiIupMxh0tmWQqlvOB7NtWawiLg2vVlORMSF2B0mnY29FIVfZXUUERHLqQiLiLiQ0uw0omwnKLtCo8EiIirCIiIupPDAWgACYrpbnERExHoqwiIiLsQrbSN2bLg119QIEREVYRERF9IsdxvHvVqBZyOro4iIWE5FWETEReQWFtPOsYes4I5WRxERcQoqwiIiLiLj4A4CjAJKmmpahIgIqAiLiLiMov2rAfBo2c3iJCIizkFFWETERbgf3UCO6UNwS91KWUQEVIRFRFzCruO5OI6s4ycjhrAAH6vjiIg4BRVhEZEGbsWeDO6a/D2tzYNEd07C3U0/+kVEQEVYRKRB+2TdYUa8v5Zefqm44yCsXQ+rI4mIOA0VYRGRBqjU7uC1b3by+GdbuKZ1EyZ0KyrfEZFgbTARESfibnUAERGpWUt3pfHXr34iJS2POxKa81JiKe4z34SwOPALtTqeiIjTUBEWEWkg9qbnMeGrn/huZxotm/gy5Xdd6eezC+OjO8G3CQybaXVEERGnoiIsIlLPZReW8taSPXyw6gDeHm48ddOVjOgRhVfKQphxLwS3gt/NhYArrI4qIuJUVIRFROqxj9cd4pWFuzhVUMLQhEhG944k9PC38MMnsPw1aNYZhn8KvsFWRxURcToqwiIi9dSU5Xt5acFOukUF89yANsQf/xL+czvknSg/oFUSDJ0OXv5WxhQRcVoqwiIi9dAn6w7z0oKdDOwQzpsdDmD7fCSc2g+R3eG29yC0LTQKBcOwOqqIiNNSERYRqWcWbjvOk59vZlTkQUbnTMT2+VYIaw93fgJtblD5FRGpJhVhEZF6ZNXeDN6cNZ95fh8Qn74VglrCre9C/O1g09LwIiIXQ0VYRKSeKC6zM2bOFt7zeodY90zo9zpcdQ+4e1odTUSkXtLwgYhIPfFJ8hHcsg9wpWMPtmsfhW5/UAkWEbkMKsIiIvVAUamdf32Xwp+abCrf0H6wtYFERBoAFWERESdnd5h8svA7+ubPZ7CxDCITISjS6lgiIvWe5giLiDip49lFfLp2H95r3uR3pZ/i5VEGuUDS/1kdTUSkQVARFhFxInaHydJdacxae5jMXSt52X0KbW1HSI28mdDfvIinXxPdJU5EpIaoCIuIOIHUrEI+WXeYT5IPk5WdxbM+n/Nbz6+w+zWFgR8T0ba/1RFFRBocFWEREQutP3iSf36XwrLd6ZjAnyIP85DbW/gWpELC73HvOw68AyxOKSLSMKkIi4hY5GR+CSPeX4e3hxsPXRfF70tnErD+n9AkBoZ+DS1/ZXVEEZEGTUVYRMQiby7eTUGJnXl3tSB66cNwZG35DTL6vwyevlbHExFp8FSERUQskJKWx/Q1h3gxdj/Rn/4JHA647T3ocLvV0UREXIaKsIiIBWbP/ZxJHp8y6MAyuKIz3P4faNLa6lgiIi5FRVhEpI6l5RQx4ugLNDcyIHEk9HsB3L2sjiUi4nJ0ZzkRkTq2e9cOmhsZHL7qcbjpZZVgERGLqAiLiNSx3N3LAQjpPMDiJCIirk1FWESkjvkeW0MejfBp3sHqKCIiLk1FWESkDhWW2AnMS+F4o1iwuVkdR0TEpakIi4jUoa+3HcPdUUJwUGOro4iIuDwVYRGROjR73WEauTloHNDI6igiIi5PRVhEpI7sS89j7f6TNPYGw83T6jgiIi5PRVhEpI78sCcDT0oJKMsEn2Cr44iIuDwVYRGROnIip4hebtuwleZD7I1WxxERcXm6s5yISB05kVPMIK8N4BEA0b2sjiMi4vI0IiwiUkcycvK5zlwHsf11NzkRESegIiwiUgcWbjuOff8KAswcaDfQ6jgiIkI1i7BhGP0Nw9hlGEaKYRhPnue42wzDMA3DSKi5iCIi9duSn07w0KwN3BmwGdPdB2L6WB1JRESoRhE2DMMN+BdwExAH/NYwjLhzHOcPPAKsqemQIiL11bLd6YycvoF24X70d0vGaNMXPLWGsIiIM6jOiHA3IMU0zX2maZYAs4FB5zhuPPAKUFSD+URE6q31m7ew5qPneSJgIZ/EfIMt7zi0+43VsURE5LTqrBoRARw+4/kRIPHMAwzDuAqINE3zK8MwxlR1IsMwHgAeAGjRosXFpxURqSdM0yRn/lM87rYCCoG1gG8TLZsmIuJELnv5NMMwbMAkYMSFjjVNcwowBSAhIcG83GuLiDirNbtT6Va6jgORg4i6+9/lG908wU2rVoqIOIvqTI1IBSLPeN789Laf+QPxwFLDMA4A3YF5esOciLiyLUs/o5FRTLNe94Cnb/lDJVhExKlUpwivA9oYhhFtGIYnMAyY9/NO0zSzTdMMMU0zyjTNKGA18BvTNJNrJbGIiJNLyymi6ZGFFLgH4tn6OqvjiIhIFS5YhE3TLAMeBL4BfgI+MU1zu2EYLxqGoXd9iIj8wuKth7jetoHSNgM0Ciwi4sSq9RPaNM0FwIJfbHuuimOTLj+WiEj9VbTzW/yMIsyut1sdRUREzkN3lhMRqWGRx74lz+aPEd3L6igiInIeKsIiIjXoVHYu3UvXcjjsenDzsDqOiIich4qwiEgNMU2TTz/5EH+jEK9Ot1odR0RELkBFWESkhvzr+xSCDy2gyD2AVt0GWB1HREQuQG9nFhGpAV9tOcZb325ns+9GvOIHaVqEiEg9oBFhEZHLtC01m9FzNnFP0wP4OPIx4gZbHUlERKpBRVhE5DJ9knwYA4PRETvAKxBaJVkdSUREqkFFWETkMpXaHTT2MvHeuxCuvBncPa2OJCIi1aAiLCJymcrsJt3ZBkXZEHeL1XFERKSaVIRFRC6T3WHSx1wFXgHQurfVcUREpJpUhEVELkNhiZ3kfWn0cqyFtjeBu5fVkUREpJpUhEVELsPbS1OIyk3G38zTtAgRkXpG6wiLiFyi/Rn5vLNsHx+GboNCf2h9vdWRRETkImhEWETkEpimyXNfbqORu4NuxT9C2/7g4W11LBERuQgqwiIil+Cd5fv4YU8G78WsxFZ0EjoOtTqSiIhcJBVhEZGLtHRXGq8s3MnI2By67H8H4m+DNv2sjiUiIhdJRVhE5CIcyMjn4Vkb6RTuyZi81zH8wmHAG1bHEhGRS6AiLCJSTQUlZfzhw2TcbAYftfgK28kUuOVt8GlsdTQREbkEKsIiItX03c409qTl8X7PbPy3vA/dR0GrJKtjiYjIJVIRFhGppq1Hsglzy6fT+rEQFgd9nrM6koiIXAatIywiUk1bj2Txt0bTMAoy4a5PtVyaiEg9pyIsIlINpmnS4+h79GAl9H0BmnawOpKIiFwmTY0QEamG3Tu3MYo5nAxsD796yOo4IiJSA1SERUSqIfeHyZSZNoyh08HmZnUcERGpASrCIiIXUpzHlUe/YK3PtTRu1srqNCIiUkNUhEVELiBj1Yf4kc/J+PusjiIiIjVIRVhE5HwcDjyTp7DFEU1ct75WpxERkRqkIiwicj77viMgfz8fOW6iZYif1WlERKQGafk0EZHzWfMO2W6N2e7fBzebYXUaERGpQRoRFhGpSkYK7PmWuW79iQwLsjqNiIjUMBVhEZGqrH0Hu+HOv3J6cnVUsNVpRESkhmlqhIjIuRRlU7p+OvPKutOzS3vu6xFtdSIREalhGhEWETmHjfP+iYe9gF0t7+LV2zti0/xgEZEGR0VYROQX5m86TPD2aez2as/oEXfg7qYflSIiDZF+uouInGHxjhMs+/RtWhpptBwwBi933U5ZRKSh0hxhEZHTVqZk8JeZq/nOcw72sE54xQ+yOpKIiNQiFWEREWD9wZPc/0Eyj/gtI6woHW6YCjb90kxEpCHTT3kRcXm7T+Qy4v11tA6w8wBzoVVvaJVkdSwREallKsIi4vK+3JRKfnEZM9uvxVZ0EvqOszqSiIjUARVhEXF5ZQ6TCPdsAjZOgfjboVlnqyOJiEgdUBEWEZfncJiMsn0O9hK4/hmr44iISB1RERYRlxeQf5DbWQIJ90FwK6vjiIj8f3t3Hh9VefZ//HNlspAAYQ1bAEHFIiouoLXWonXFlWrd91Yfa9XurT992qePtdVa1y5a61q1KlRxQ0VZ1Lo+omwKsm+yhwQIS0L26/fHOZHJmA1IcpLM9/16zWvm3HPPzHXmQPLNPfe5R1qIgrCIJC135/EPlrPPnHspT8mAUTdEXZKIiLQgLZ8mIkmpuKyCG5+fw4rP3mNCxjRKjvoVdMqJuiwREWlBCsIiknSW5W/nmqdmsGTDNt7t/TJe1pMOo34SdVkiItLCNDVCRJKGu/Py7DWced8H5G8rZcLJJfQvnI4d8/8go3PU5YmISAvTiLCIJIUlG7bzvxPm8sGSjRw8oCv/GNOXvuNGQ499YcQVUZcnIiIRUBAWkXatuKyCv765hEffX0aHtBi3jDmAi0f0Jvb4qVBWBJe9DKnpUZcpIiIRUBAWkXbJ3Xlj7np+/+o81m4p4ZwR/bnxlKH07JgOL10La2fCBc9Ar/2jLlVERCKiICwi7U5xWQXXPDWTnCXP84vO6/nmiB70yc6ED4Bt62HueDj2Jhh6WtSliohIhBSERaTdeXP+BpYt/pwnMh6EinRscVrNDodcojWDRUREQVhE2p+C7aVcEnsTLAX78Szokht1SSIi0gpp+TQRaXe2bNnK+bG3g6kPCsEiIlIHjQiLSLuTu/Z1utl2OOLqqEsREZFWTCPCItLuDNzwNutT+sCgo6MuRUREWjEFYRFpV7YUlTG4dAGbehwKZlGXIyIirZiCsIi0K9PnzKGXFdJp769HXYqIiLRyCsIi0m6UVlSydNbbAPQ78FsRVyMiIq2dTpYTkTavvLKK8TNW88ybn/BAyQNsTc8hu+/wqMsSEZFWTkFYRNqsisoqXpy1hr++tZj8TYVM6HQ7fVOLSLnidUhNj7o8ERFp5RSERaTNqaxyXv1sLX+ZuphlBUUM79eZ5/cdS87qxdgFz0DuoVGXKCIibYCCsIi0KZ+tLuQXz37K4g3bGdqnMw9eOoKT1j6AfTAZTv4jDD016hJFRKSNUBAWkTbl9tcXsLm4jPsvOoxTDuxDyuJJ8MGfYeT34cgfRl2eiIi0IVo1QkTajM1FZUxbvonzRg7gtOF9Sdm+Hl6+FvocBKNv17rBIiKySxSERaTNeHPBBiqrnNEH9oGqKnjxB1C+A777GKRmRF2eiIi0MZoaISJtxhtz19OvSwcOyu0STIdY/g6c+TfI2S/q0kREpA3SiLCItAmVVc5HyzZy7NBe2JqZ8NYf4ICz4NBLoy5NRETaKI0Ii0ibsCx/O9tLKziiz0XVzwAAH2tJREFUbxo8fwl07gen/1nzgkVEZLcpCItImzB7VSEAxy+9HQpXwfdeh8yuEVclIiJtmaZGiEib8OnqQi7M+JDOi1+EY2+EgV+PuiQREWnjGhWEzWy0mS00syVmdmMt9//czOaZ2Wdm9qaZ7dX0pYpIsiopr+TzObP435RHYa9vwrd+EXVJIiLSDjQYhM0sBtwPnAIMAy40s2EJ3WYBI919ODAeuKOpCxWR5DX+42X8rvweUtPS4eyHICUWdUkiItIONGZE+Ahgibsvc/cyYBwwJr6Du7/t7sXh5kdA/6YtU0SSVXllFfbWHxiespzYd+6DLvrxIiIiTaMxQTgXWBW3vTpsq8uVwOt7UpSICEBVlTP55ae4uPIlVu1zETbszKhLEhGRdqRJV40ws0uAkcAxddx/NXA1wMCBA5vypUWkHXF3Js/LY+rE57ll+82sSNubgefdHXVZIiLSzjQmCK8BBsRt9w/bajCzE4BfA8e4e2ltT+TuDwEPAYwcOdJ3uVoRadfcnXcW5XPPlEV0WPMRT2TcQXn2AAZe/QYpGVlRlyciIu1MY4LwJ8AQMxtMEIAvAC6K72BmhwIPAqPdfUOTVyki7d5HyzZy9+SFfLJiM6dmL+evWXcR6zaIzCtehU69oi5PRETaoQaDsLtXmNn1wCQgBjzm7p+b2S3AdHefANwJdAKes+Bbnla6uybziUiDNmwt4efPfsr7SwronZ3BP46p4ORZf8S69ofLX1EIFhGRZtOoOcLuPhGYmND227jbJzRxXSKSBMoqqrjmqRksWL+N35y2P5cO2EDGM1dAp95BCO7cO+oSRUSkHdNXLItIZG6bOJ+ZKwu5/6LDOK3HWnjyXOiUA1e8Ctl9oy5PRETaOX3FsohE4qVZa3j8wxVcefRgTuu5Hv51FmR1h8tfhex+UZcnIiJJQEFYRFrcorxt3PTCHA4f1I0bDymDJ78DHboEIbhLfcuUi4iINB0FYRFpUZVVzg3jPyMzPcaDJ2aQ9vR3IKNzEIK7Dmj4CURERJqI5giLSIt66qMvmL2qkMdGZ9J9/DmQ1jGYE9xtr6hLExGRJKMRYRFpMeu3lHDnpIVcuNc2vv3xVZCWCVe8At0GRV2aiIgkIQVhEWkRlVXOb16aQ7+qtfxh66+xWHqwRFr3vaMuTUREkpSmRohIs6uorOKG8Z8xdf4G3u3/ArFt5XD5G9Bjn6hLExGRJKYRYRFpVuWVVfxk3GxemLWGe7++nYEF78K3fgY9h0RdmoiIJDkFYRFpNqUVlVz79Exem7OO35w6lLMKHoTsXPj6NVGXJiIioqkRItI83J3rnp7J1PkbuGXMAVyWPQvWzIAxfw9OkhMREYmYgrCINIstO8qZOn8DPxi1N5cd3g/+fhb0OgAOviDq0kRERAAFYRFpJlUeXPft0gFmPA6blsFFz0FKLNK6REREqmmOsIg0iyoPknBGVRG88ycY9C0YcmLEVYmIiOykICwizaIqHBI+YMWTUFwAJ94CZhFXJSIispOCsIg0i4ffW0YOmzngiyfhwO9C7mFRlyQiIlKD5giLSJN7Z1E+D7+3nOdyJxHbXAHH/U/UJYmIiHyFRoRFpEkVbC/lF89+yvE9NzNy02tw+JXQfXDUZYmIiHyFRoRFpEmUVlTyf0s38ve3l7K1pJw/938ZK+8Io34VdWkiIiK1UhAWkd22qaiMtxdsYOr8PN5dlE9RWSWZaTH+MaqMzh9ODqZEdOwZdZkiIiK1UhAWkV2yNH87U+flMXV+HjO+2EyVQ+/sDL5zaC4nDOvNNwZ3p8OTp0DnvnDktVGXKyIiUicFYRGpV0VlFTNXFjJ1fh5T5+WxrKAIgGF9s7n+uCGcuH9vDszNxqqXRps3AVZ/DGf+DdKzIqxcRESkfgrCIlKrwuIy/jhxAZPmraewuJy0mHH6XpXc3/119soqJSs9BtuAjxMeuOJ9yBkKB18URdkiIiKNpiAsIl+xOG8bVz05nXWFJZw2vC+nDOnIMflPkfHxA0GH7L51PzgjG06/B2L68SIiIq2bflOJSA1vLcjjx2Nn0yEtxtirRjBi46vw5m1QlA/Dzw9OgOs6IOoyRURE9piCsIgA4O48+O4y/vTGAg7ol80T39pKj4lnQP4CGHgUXPRvyB0RdZkiIiJNRkFYJMmVVlTy4dKNjJ22ksnz8vivr+3gxpSHib30NnQbDOf9C/Y/A6pPhhMREWknFIRFktCW4nLeXriBKfPy+M/CDRSVVbJX+jZeG/wGw1a+jGV0hpP/CIdfBanpUZcrIiLSLBSERZLE2sIdTJmXx+R565m2bBMVVU5O5wzOObgHl9trDF7wMJZXAkf8AI65AbK6R12yiIhIs1IQFmmn3J0F67cx+fM8psxfz9w1WwHYJ6cj/zVqb07aP4eDN08m5a0fw9Y1MPR0OOF30HPfiCsXERFpGQrCIu3M8oIixn28ktfmrGP15h2YwWEDu3HT6CGcZe/SK/9D2A68vgjWz4G+h8DZD8Ggo6MuXUREpEUpCIu0A+WVVUydl8fT01by/pICYinGqCE9uf7b+3L8/r3J2TwLXr8K1n0K2bmQlglpWXDWg3DQeZCSEvUuiIiItDgFYZE2bE3hDsZ9vJJxn6wif1spuV0z+eVJ+3HeyAH0yu4AW9bA5OtgznPQuR+c/QgcdI5WgBAREUFBWKTNqaxy3lm0gac/WsnbCzfgwHFf68XFRw7kmP16EUsxKC+Bd++E9+6BqkoY9Ss4+meQ3jHq8kVERFoNBWGRNqKkvJK3Jv6b1E+fobS8nPNTY/yqXxYDe2SRlRaDOQQXgDXToXBlsP7vSX+AboMirFxERKR1UhAWaeXKK6t49pOVbJxyN9dV/IvtsS7EunSjY0YqBrCxlgdl58KZf4O9j23RWkVERNoSBWGRVqqyynnl07XcN3kO123/KxfHPmDjoFPpcfEjmuIgIiLSBBSERVoZd2fKvDzunryILXkreLLjX9gvtgT/9m/oMeqXOtFNRESkiSgIi7Qin6zYxK2vzWf2qkLO6LaSO7vcRYaXwrljsaGnRl2eiIhIu6IgLNIKrN5czO2vL+DVz9bRJ7sDzx2+iJGf34p1HQAXjIVeQ6MuUUREpN1REBaJUFFpBf94ZykPvbsMM/jZtwdzbdkjpM14FPY5Ds55DDK7RV2miIhIu6QgLBKBqirnxVlruGPSAvK2ljLmkH7cNKonfSb/EFa8B0f9CI6/GWL6LyoiItJc9FtWpAW5O/9ZlM9rE1/h2E3/5t7MVPb/WjbdLA3GzYSifDjrITj4/KhLFRERafcUhEVaQGWVM3HOOh74z1LmrdvKo1njOTZtNild9saKN0Ex0CUXzn8SckdEXa6IiEhSUBAWaUalFZW8MHMND76zlBUbi9k7pyN3nj2M496ciw07D8bcF3WJIiIiSUtBWKQZbC+tYOy0lTzy/jLytpZyUG4XHrj4ME46oA+xVf8HpVthyIlRlykiIpLUFIRFmsj20gqmLdvIe4sLeHHWGrbsKOcbe/fgrnMP5uh9emCbl8Pc52DWU5CSqq8/FhERiZiCsMhuKq+sYvaqQt5fXMAHSwqYvaqQiionIzWF0/dN49ohJexT9hZ8dAc8PwNKCoMHpnUMVoXo0CXaHRAREUlyCsIijeTuLMzb9mXwnbZ8E8VllWRaGWf2LuCHQ1YznCX02DKHlBVfwArAUqDXMBg2JjgJrv9IyBkKKbGod0dERCTpKQiL1GNN4Q4+WFIQXjaycfsO9rZ1nJS9imtyVjG0chHZWxdihRVQCGT3h9zD4PArIXck9D0YMjpFvRsiIiJSCwVhkQRlFVU8+M5SXpy1hmUFRQCcmTWXpztMYnCnhaRXbIdSwDtD7qFw4I+Dkd7cEdC5T7TFi4iISKMpCIvEWbh+Gz9/djafr93K0fv25KIj+jNm6zPkTL8b0gbAsPOCkd7cEdBzP0hJibpkERER2U0KwiIEX3jx8HvLuGfyIjp3SOXBS0dw8j6Z8OI1sHAiHHwhnH4vpGVGXaqIiIg0EQVhSXorCor45XOfMv2LzZx8QG9uPesgeu5YAQ+fDpuXwyl3wBFXg1nUpYqIiEgTUhCWpDZ1Xh4/GjuL1Jhx7/kH851DcrEFr8GLPwhGfy+bAIO+GXWZIiIi0gwUhCVpVVY5t7w6j4Hds3j8+4fTt3M6vH0rvHtnMAf4vH9Bl9yoyxQREZFmoiAsSWvq/DxWbirm7xcfRt/0EnjmUlgyBQ69FE69C9I6RF2iiIiINCMFYUlaj76/nNyumZzUcyM8dAlsWR2cEDfie5oPLCIikgQUhCUpzV2zhY+Xb+LRkatJfewSyOgM35sIA46IujQRERFpIQrCkpQmzFrJf6eN5fi5r8CAr8N5T+rLMERERJKMgrAkHS/ayIkzr+Pw2Kcw8koYfTukpkddloiIiLQwfS2WJJd1n1H+j2MYXvk5Hx14C5x+j0KwiIhIktKIsLRr7k7+9lJWbSqm8tNnOXT2b9lGZ64s/y0Pn3xN1OWJiIhIhBSEpc0rKa9k9eZiVm4q5ouNwfWqTcH1yk3FlJeXc1PqM1yV+jrTqoZyS4cbOPzIoeR0zoi6dBEREYmQgrC0evGjutVBNz7s5m0trdE/Kz3GwO5ZDOrRkdGDUrlo5W/ps3k6W4ZfySGn3cZrGVofWERERBSEpZVoaFS3pLzqy75m0De7AwO6ZzFqSA4Du2cxsEdWcN09i+4d0zEzWDsLxl0NxQVw1kN0Ofj8CPdQREREWhsFYdktVVVOSUUlxWWV7CirpKS8kh3l4XZ5JSVlO7dLyoM+NbbDts3FZbWO6nZMjzEgHNUdNSSnRtDN7ZZJRiwFSrdBUT4UFUDRQtiQD8sLwrYNsGAidOoN358E/Q6J6J0SERGR1kpBuB2qDqk7yr4aPIvjQmp1247E7dquw8cVh22lFVUNF5IgLWZ0SIuRlR4jMy1Gh7QYXTLTvhzVHdQ1lcFZO+ifXkSXqkKsaE0YavNhfQEszY8LvvlQWVr7C3XoAh1zYOhpwVcld+yxh++oiIiItEcKwi0sPqQ2FDwTQ2pJ+c4R2BrbCSOwexJSM9NiZKbXvO6alVbzvur7a+lbo0+qkVW5lazyzWSUbiJ1R8HOEFsUF2rX5cOSAijdUntxsQzo1As69gyuex8Q3O6YE17ibmf11HJoIiIi0igKwnESQ2p9wbN6OkBx3H3VI7BfbldPBagRZnc9pKam2FcDZ3jdJzuNDukxsuLavhx1TY99GWC/HIVNr307LdaIJaXdoWx7GGA31gy0+QU1w21RfjA312vZX0uBrB47Q2y/Q74aaOO30zsFE4NFREREmlBSBeH567Zy28T5NaYK7NjDkBpLMbLCQBn/kX9mWozendO+DJrV4bNDQ6OoaTH6Tr+TzII5xFKMlBRr+FtPKsNLyW68KQ3xKigp3BluK+p4kYzsncG1+2AYcHjtI7YdcyCzG6TEmqFYERERkcZrVBA2s9HAX4AY8Ii7355wfwbwJDAC2Aic7+4rmrbUPecO20oqyEyL0atz2ldGWOPnr1aPlmbVdl/cdqNGUndVajlUbGv6591dWT0gZ2jdI7ZZPSFNS5KJiIhI22LuXn8HsxiwCDgRWA18Alzo7vPi+lwLDHf3a8zsAuAsd693raqRI0f69OnT97R+EREREZF6mdkMdx+Z2N6Y4cwjgCXuvszdy4BxwJiEPmOAJ8Lb44HjzTSpU0RERERar8YE4VxgVdz26rCt1j7uXgFsAbRmlYiIiIi0Ws0wwbVuZna1mU03s+n5+fkt+dIiIiIiIjU0JgivAQbEbfcP22rtY2apQBeCk+ZqcPeH3H2ku4/MycnZvYpFRERERJpAY4LwJ8AQMxtsZunABcCEhD4TgMvD2+cAb3lDZ+GJiIiIiESoweXT3L3CzK4HJhEsn/aYu39uZrcA0919AvAo8C8zWwJsIgjLIiIiIiKtVqPWEXb3icDEhLbfxt0uAc5t2tJERERERJpPi54sJyIiIiLSWigIi4iIiEhSUhAWERERkaSkICwiIiIiSUlBWERERESSkoKwiIiIiCQlBWERERERSUoKwiIiIiKSlBSERURERCQpKQiLiIiISFJSEBYRERGRpGTuHs0Lm+UDX0Ty4i2rJ1AQdRHSZHQ82xcdz/ZFx7N90fFsX6I+nnu5e05iY2RBOFmY2XR3Hxl1HdI0dDzbFx3P9kXHs33R8WxfWuvx1NQIEREREUlKCsIiIiIikpQUhJvfQ1EXIE1Kx7N90fFsX3Q82xcdz/alVR5PzREWERERkaSkEWERERERSUoKws3EzEab2UIzW2JmN0Zdj+w+MxtgZm+b2Twz+9zMfhJ1TbLnzCxmZrPM7NWoa5E9Y2ZdzWy8mS0ws/lm9o2oa5LdZ2Y/C3/WzjWzsWbWIeqaZNeY2WNmtsHM5sa1dTezKWa2OLzuFmWN1RSEm4GZxYD7gVOAYcCFZjYs2qpkD1QAv3D3YcCRwHU6nu3CT4D5URchTeIvwBvuPhQ4GB3XNsvMcoEfAyPd/UAgBlwQbVWyGx4HRie03Qi86e5DgDfD7cgpCDePI4Al7r7M3cuAccCYiGuS3eTu69x9Znh7G8Ev2dxoq5I9YWb9gdOAR6KuRfaMmXUBRgGPArh7mbsXRluV7KFUINPMUoEsYG3E9cgucvd3gU0JzWOAJ8LbTwDfadGi6qAg3DxygVVx26tRcGoXzGwQcCgwLdpKZA/9GbgBqIq6ENljg4F84J/hVJdHzKxj1EXJ7nH3NcBdwEpgHbDF3SdHW5U0kd7uvi68vR7oHWUx1RSERRrJzDoBzwM/dfetUdcju8fMTgc2uPuMqGuRJpEKHAY84O6HAkW0ko9cZdeF80bHEPyB0w/oaGaXRFuVNDUPlixrFcuWKQg3jzXAgLjt/mGbtFFmlkYQgp929xeirkf2yDeBM81sBcG0pePM7KloS5I9sBpY7e7Vn9KMJwjG0jadACx393x3LwdeAI6KuCZpGnlm1hcgvN4QcT2AgnBz+QQYYmaDzSydYKL/hIhrkt1kZkYw/3C+u98TdT2yZ9z9Jnfv7+6DCP5vvuXuGnFqo9x9PbDKzL4WNh0PzIuwJNkzK4EjzSwr/Nl7PDr5sb2YAFwe3r4ceDnCWr6UGnUB7ZG7V5jZ9cAkgjNeH3P3zyMuS3bfN4FLgTlmNjts+293nxhhTSKy04+Ap8OBh2XA9yKuR3aTu08zs/HATIIVe2bRSr+RTOpmZmOBY4GeZrYa+F/gduBZM7sS+AI4L7oKd9I3y4mIiIhIUtLUCBERERFJSgrCIiIiIpKUFIRFREREJCkpCIuIiIhIUlIQFhEREZGkpCAsIl9hZjebmZvZpFruG29m/4mgrF1mZseG+3FgPX0GhX2qL9vN7FMzuyquzxwze6We53jVzNr0WqdmdkW4/52a6PnONrMlZhYLt6uPxcbE1zCz681sj5YwMrMcM/urmX1sZmXhF6bU1fe/zGyxmZWY2QwzO76WPrlm9qKZbTOzAjO7z8yy4u7PNLMNZvatPalbRKKlICwi9TnJzA6PuogW8kvgG8BZwKfAw3Ff7TqW4L3olvigsO2ksI8AZpYC3ALc6e6VCXd3B37YDC+bC5wPrAdm19XJzC4E/gE8CZwCfA68Gv/HUvhNkpOAvQi+dOUnwLnErWfr7juAvwG/b+odEZGWoyAsInXZBMwBft0cT25mmc3xvHtgobt/5O5TCL71aD5wWXjfOCAdOLuWx30XSENBON7xwD7AM7Xc9x/g52bWoYlf8zN37+3uZwLv1tPvZuAJd/+9u78NXAEsAW6M63MOsD/wXXd/zd2fJvjSjovMbEhcv8eBUWZ2UNPthoi0JAVhEamLA7cCZzb0i97MDjGzN82s2Mw2m9nTZtY77v7q6QcXm9mTZlYIvBLXfoGZ/dPMtprZ6uqRWDO7wczWmlm+mf0pHGmsfs6hZjbOzFaFr/u5mf00vs9u73jwTUNzgAHh9jJgGsHoYKILgBnuvrie9+doM3sv3L+tZjbbzM6Nu/8yM3vfzDaF79/bZjYy4TkeN7PpZnaamc0L9/k1M+tuZvuGjykK+wxPeKyb2c/N7C/haxSa2d/Cb2Krk5l1MLM7wve4NJwycmpD7x/BHxKT3X1bLffdQTAqfFUt9+02d69qqI+Z7Q3sBzyb8LjnCEaHq50CfOLuy+PaXgLKgNFxj10FfMLOP5hEpI1REBaR+jwHLKaeUWEzyyEY5csCLiIYOTsGmFJL0LoL2EbwMfNtce1/AtYRjK6+BzxhZncDRwDfB/4M3EDNr+TMBRYC1wKnAg8DvwP+367vZq0GAvFBaCzwbTPrVd0Qhv1jqWc02MyygVcJvvr3uwSjjf8CusZ1G0TwUf25BO/hKuC9MLgl1nQL8BvgauAogo/rx4WXc4BUYJyZWcJjfwH0By4G/hA+/ta6dx+A8QQjprcBZxCEvglmdkgDjzsO+LCO+1YR7OsN4RSEWplZzMxSG7js6u+woeH1goT2+UD38N9ydb8afdy9DFga9xzVPgRO2MU6RKS1cHdddNFFlxoXgo+PC8LbVwCVwH7h9njgP3F9bwcKgey4tq8TjChfGG4PCrdfTHid6vZ/xrVlA+UEATwW1/4x8O866jWCAPjfwLK49mPD5z+wnn2truHM8Dm6AT8FSoFRcf36hu/DdXFt1wNVQP96nn9k+PydG/nep4R1LAB+G9f+OFAB7BPXdkf43JfFtZ0atu0f1+bh86XEtf0aKAa6xx1nBzqF28eH28ck1Pcu8Fw99fcLH3daQvuXx4Jg2kQFcGXc++gJ/VeE/eu73FxHDXcBK2ppvzh8XNeE9hPC9up/44uBP9fy+PeBZxLargj3pUOU/2d10UWX3btoRFhEGvIUsBK4qY77jyD4GHxrdYO7TyMIMkcn9H2tjud4M+6xW4F84B2veaLVEoJRYODLj+1/Z2ZLCEJrOcEI52AzS23EfiV6OXyOTcC9wK/c/cu5pu6+jmDk+/y4x5wPvOfuq+t53qXAduAZMxtjZl0TO5jZ/uEKBXkEYbsc+BrBx/jxVrj70rjtJeH1W7W05VLTy15z+sALQCZBMK3NCQQnnn0QPwpLcKxG1vEYgD7hdUFdHcJ9GAfcaOGqErU4Azi8gctDdTy2JRUAMSCnoY4i0vrszi8LEUki7l5hZncAfzWzm2vp0pfgzPtEeQRzQRPbalOYsF1WR1v8CVZ/Iphn+jtgZth/DMG0gQ4E4XNX/IxgxK8XwWjpXWb2jrt/GtdnLPCQmeUSjEJ/k2BqRp3cfbOZnUgwyv4skGJmk4EfufsyM+sMTCZ4b34OfAGUAI8k7C/U/p4ktle3JT52Qx3bfesovSdBqC2v5b7ElSDiVb9uaT19IJhuMZeaf1jEm0fwHtenwXnBCTaH112o+Z51S7h/c9gnUTeCFUXiVe9nU5/8JyItQCPCItIYjxEEp9rm364jCI+JehOMrsbbo7ViE5wL/M3d73D3qe4+neAj6t21xN2nu/tE4HRgK8G0j3jPEwTD88NLJcFUkXp5sBrFaIJ5wWcTjPRWr6jwDYK5u5e4+9Pu/n64L7UFsT2ReIyqt9fV0X8TsIbaR2KPrOd1qo/5V0a+47n7POBFgukstQXepQTvdX2X39b3GrWonvebOM93KLDJ3fPj+tXoE85335uvzi+u3s/Ef+si0gZoRFhEGuTupWZ2F/BHYAY1RwmnAT80s84erhJgwdrDgwhGWJtLJnGjjuFH7LWt6rDLwlHcPwF3mNlwd/8srn1S+DoGTHH3OqcA1PK8OwhWyziQnVNNqpeRi9+Xowjevxl7vDM7jTGzm+KmR5wN7CAYla3NmwQn2G1398TwV58VBKPSgwmmktTnVoJ9PKuW+84AMhp4/NpdqItwBH4RwR9Rk+DLNY/PBV6P6/o6wVJpe7n7F2HbmWE9byQ87SBgo7tv3JVaRKR1UBAWkcZ6kGD07ijgnbj2ewi+IGFSGB47EYykziEYQW0uU4DrwjnCm4DraDg47YoHCNaW/RVwaVz7WHaO5ja4bJaZnUaw8sVLBHOtc4EfsHNe70cE0zgeDqeg9CeYRrFmj/egps7Ac2b2MHAA8D/A/e5e10jmFIKwOCU8rp8TnMh4CMGJYbXOGXf3EjObAYwA/llfQe4+08xep+bSZdX3zWncbu1kZueEN/cDsuK234kb7b0ZeMqCb577gGCptyEEq3VUG08wPeYFM/sfgtH5ewlOlEtcJm8kda+QISKtnKZGiEijuHsxQRhIbM8Hvk0wr3UscD/BEmgnerDkVHP5Ufg69xNM3ZhLMGLdJNx9O/AX4AIzGxB31wSC1RZKCMJtQ5YQTAm5jWAu8B0Eo4rfD18nj2BEsg/BCXs/Ba5h50lvTeVugmkQYwmmFDxK8IdNrdzdCUaNHwtrmkTwx9A3aHik/wXi1tttwB8a2a8xngsvZxCcvFa9fUB1B3cfS/D+XkFwHIYDp7v73Lg+5QT1ryKY130fwR91V8e/WHjy4PE07x98ItKMLPhZJyIi7ZWZOcHJefe10Ov1Jhj9PtrdP2mJ14yCmZ1MEJT7uXtR1PWIyK7TiLCIiDSpcJT7EeAnUdfSzH4G3KsQLNJ2KQiLiEhz+D0wv551gts0M8sE/o9gjryItFGaGiEiIiIiSUkjwiIiIiKSlBSERURERCQpKQiLiIiISFJSEBYRERGRpKQgLCIiIiJJSUFYRERERJLS/we02O40WRya8QAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"#https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html\n", | |
"from scipy.stats import ks_2samp " | |
], | |
"metadata": { | |
"id": "E_vYAvV-mFS7" | |
}, | |
"execution_count": null, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"ks_2samp(sample_1, sample_2)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "vO41B-LPmM7n", | |
"outputId": "e20a106c-72a5-47b7-c319-ceb88a7a760d" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Ks_2sampResult(statistic=0.09, pvalue=0.8154147124661313)" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 25 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"Alternative: $F_1 < F_2$ - Пример одностороннего теста" | |
], | |
"metadata": { | |
"id": "8xCfjgXrqHxP" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"y_ecdf = ecdf(sample_1)\n", | |
"plt.plot(np.sort(sample_1), np.sort(y_ecdf), label='ECDF N(5,2)')\n", | |
"plt.plot(np.sort(sample_1), norm(4,2).cdf(np.sort(sample_1)), label='CDF N(4,2)')\n", | |
"plt.legend(fontsize=15)\n", | |
"plt.xlabel('Normal RV sample (N=100)', fontsize = 15)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 520 | |
}, | |
"id": "_2dtQBJfnQyV", | |
"outputId": "eb2c0159-1221-406d-a252-dd86bc591bfe" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, 'Normal RV sample (N=100)')" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 26 | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 864x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"kstest(sample_1, norm(4,2).cdf, N=100, alternative='less')" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "U3r3b70LqluS", | |
"outputId": "6ac62ece-450c-4599-cfb6-82ffd4064e55" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"KstestResult(statistic=0.24158215771226887, pvalue=6.358711841801269e-06)" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 27 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"# Тест на независимость" | |
], | |
"metadata": { | |
"id": "xKKSCulj8jGY" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Пример 1\n", | |
"\n" | |
], | |
"metadata": { | |
"id": "nuawFakP8m2e" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"\n", | |
"\n", | |
"Source: Wasserman L. All of statistics, p.241" | |
], | |
"metadata": { | |
"id": "JrmDGoaQcGpH" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Формулировка теста\n", | |
"\n", | |
"$H_0:$ Тонзиллэктомия (удаление миндалин) не влияет на возникновение болезни Ходжкина, то есть, эти бинарные случайные величины независимы.\n", | |
"\n", | |
"$H_1:$ Тонзиллэктомия (удаление миндалин) **влияет** на возникновение болезни Ходжкина, то есть, эти бинарные случайные величины зависимы.\n", | |
"\n", | |
"Зафиксиррем критерий значимости: $\\alpha=0.05$\n", | |
"\n", | |
"Пусть $X$ - это случайная величина, моделирующая Тонзиллэктомию, где $X_1=1$ если процедура была проведена и $X_2=0$, если процедуры не было.\n", | |
"\n", | |
"Аналогично, для болезни Ходжкина, $Y_1=1$, если диагностирована болезнь и $Y_2=0$ в противном случае. \n", | |
"\n", | |
"В условиях нулевой гипотезы, случайные величины $X$ и $Y$ независимы:\n", | |
"- $P(X\\ and\\ Y) = P(X)P(Y)$ (по определению независимости событий)\n", | |
"- Вероятность возникновения любого варианта из таблицы: $\\hat{p}_{i,j}=\\hat{p}_i\\hat{p}_j=\\frac{X_i}{n} \\frac{Y_j}{n}$ (по MLE для [мультиномиального распределения](https://en.wikipedia.org/wiki/Multinomial_distribution))\n", | |
"- $E_{i,j}=np_{i,j}$ согласно мультиномиальному распределению\n", | |
"\n", | |
"\n" | |
], | |
"metadata": { | |
"id": "nUs-mW9kdwZq" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Рассчитаем оценку $\\hat{p}_{i,j}$" | |
], | |
"metadata": { | |
"id": "r_DAHumKk0cK" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"X_1_total = 255\n", | |
"X_2_total = 391\n", | |
"Y_1_total = 174\n", | |
"Y_2_total = 472\n", | |
"N = 646\n", | |
"\n", | |
"p_11 = X_1_total/N * Y_1_total/N\n", | |
"p_12 = X_1_total/N * Y_2_total/N\n", | |
"p_21 = X_2_total/N * Y_1_total/N\n", | |
"p_22 = X_2_total/N * Y_2_total/N\n", | |
"\n", | |
"print(p_11, p_12, p_21, p_22)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "EOxhbW-adv33", | |
"outputId": "003b16c1-2235-48c4-d3b3-8a3f354b92bf" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"name": "stdout", | |
"text": [ | |
"0.10632230731627831 0.2884145347889849 0.16302753788496008 0.44223562000977673\n" | |
] | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Рассчитаем $E_{i,j}$" | |
], | |
"metadata": { | |
"id": "a_R6tsrjnaRH" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"e_11, e_12, e_21, e_22 = p_11*N, p_12*N, p_21*N, p_22*N\n", | |
"print(e_11, e_12, e_21, e_22)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "zv_zv5B9nXwp", | |
"outputId": "7700d8fa-f5dd-4ba3-eb8b-e9c7a0328bae" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"name": "stdout", | |
"text": [ | |
"68.6842105263158 186.31578947368422 105.3157894736842 285.6842105263158\n" | |
] | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"# Тест-статистика\n", | |
"\n", | |
"Критерий согласия Пирсона (Pearson's chi-squared test) имеет вид:\n", | |
"\n", | |
"$D_2=\\sum_{i=1}^r\\sum_{j=1}^c \\frac{(n_{i,j}-E_{i,j})^2}{E_{i,j}}$,\n", | |
"\n", | |
"где $r$ - количество вариантов реализаций $X$, $C$ - количество вариантов реализаций $Y$. \n", | |
"\n", | |
"$D_2$ [подчиняется распределению](https://en.wikipedia.org/wiki/Chi-squared_distribution) $\\chi^2_{df}$, где $df=(r-1)(c-1)$ - это количество степеней свободы распределения $\\chi^2$\n", | |
"\n", | |
"Для нашего примера с двумя реализациями для $X$ и $Y$ тест-статистика будет иметь вид:\n", | |
"\n", | |
"$D_2=\\sum_{i=1}^2\\sum_{j=1}^2 \\frac{(n_{i,j}-E_{i,j})^2}{E_{i,j}}$" | |
], | |
"metadata": { | |
"id": "rt9bH837n5OD" | |
} | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Расчитаем тест" | |
], | |
"metadata": { | |
"id": "RIBsscRIquJq" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"n_11 = 90\n", | |
"n_12 = 165\n", | |
"n_21 = 84\n", | |
"n_22 = 307\n", | |
"\n", | |
"d_2 = 1/e_11*(n_11 - e_11)**2 + 1/e_12*(n_12 - e_12)**2 + 1/e_21*(n_21 - e_21)**2 + 1/e_22*(n_22 - e_22)**2\n", | |
"print(d_2)" | |
], | |
"metadata": { | |
"id": "yNfjXxqCqtUK", | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"outputId": "555373c0-27cf-4ef0-cf13-a4ad3dad7ee5" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"name": "stdout", | |
"text": [ | |
"14.95864355957614\n" | |
] | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"df = (2-1)*(2-1)" | |
], | |
"metadata": { | |
"id": "0IcCyQnkrXWy" | |
}, | |
"execution_count": null, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## $p$-value" | |
], | |
"metadata": { | |
"id": "1kHORBbwtAY1" | |
} | |
}, | |
{ | |
"cell_type": "code", | |
"source": [ | |
"# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html\n", | |
"from scipy.stats import chi2\n", | |
"\n", | |
"1 - chi2(df).cdf(d_2)" | |
], | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "tEaoGsl2rhep", | |
"outputId": "9a60ab3e-31a0-4b07-c495-d0691d85dc69" | |
}, | |
"execution_count": null, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"0.00010989348314649483" | |
] | |
}, | |
"metadata": {}, | |
"execution_count": 31 | |
} | |
] | |
} | |
] | |
} |
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