{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this post we share how to plot distribution histogram on the [Weibull ditribution](https://en.wikipedia.org/wiki/Weibull_distribution) and the distribution of sample averages as approximated by the Normal (Gaussian) distribution. We'll show how the approximation accuracy changes with samples volume increase. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Weibull distribution\n", "\n", "The *scipy* reference to the Weibull is [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as sts\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's generate Weibull ditribution and plot its histogram." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First 10 Weibull samples:\n", " [0.90366715 0.02199363 1.72656887 1.56038375 0.51431021 4.15967432\n", " 0.96637003 0.21764417 0.14502339 1.46848327]\n", "\n", "Mean of Weibull samples: 1.0226250055940325\n" ] }, { "data": { "image/png": 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oN77yUODnu7H/nmASjhEm4zgn4RhhMo5z6GN8cFUt2tEH862nkB203S21quoC4II5+bJkTVUtm4ufNV9NwjHCZBznJBwjTMZxzudjnFdjCsA64PBp60uB2waqRZImznwLhW8DRyU5Isl9gdOA1QPXJEkTY16dPqqqLUleDnwJ2Av4cFVd1+NXzslpqHluEo4RJuM4J+EYYTKOc94e47waaJYkDWu+nT6SJA3IUJAktSYyFCZhKo0khyf5WpIbklyX5Nyha+pLkr2SXJvk80PX0pckByX5VJIfNn+njx+6prmW5FXNv9UfJPl4kv2GrmkuJPlwkg1JfjCt7ZAklye5sXk/eMgap5u4UJigqTS2AK+uqocCjwPOXqDHCXAucMPQRfTsX4AvVtVDgGNZYMebZAlwDrCsqh7O6EKT04atas5cCJy4Xdty4IqqOgq4olmfFyYuFJg2lUZV/R7YNpXGglJV66vqmmZ5M6P/RJYMW9XcS7IUOAn44NC19CXJgcBfAR8CqKrfV9UdgxbVj72B/ZPsDdyPBXKPUlVdCfxyu+aTgZXN8krglHHWNJNJDIUlwK3T1texAP+znC7JFHAccNXApfThXcBrgD8OXEefjgQ2Ah9pTpN9MMn9hy5qLlXVT4F3ALcA64FfVdWXh62qVw+sqvUw+gUOOGzgelqTGAq7nEpjIUnyAODTwCuratPQ9cylJM8BNlTV1UPX0rO9gUcB76uq44A7mUenG+ZCc079ZOAI4EHA/ZO8eNiqJtMkhsLETKWRZB9GgXBRVV0ydD09eCLw3CRrGZ0GfGqSjw5bUi/WAeuqaltP71OMQmIheRpwc1VtrKo/AJcATxi4pj7dnmQxQPO+YeB6WpMYChMxlUaSMDoHfUNVvXPoevpQVedV1dKqmmL09/jVqlpwv11W1c+AW5Mc3TSdwMKbTv4W4HFJ7tf82z2BBTaYvp3VwOnN8unApQPWcjfzapqLcRhgKo2hPBF4CfD9JN9p2l5XVV8YriTthlcAFzW/yPwYOGPgeuZUVV2V5FPANYyunLuWeTwVxGwk+TjwZODQJOuANwErgFVJzmQUiKcOV+HdOc2FJKk1iaePJEk7YShIklqGgiSpZShIklqGgiSpZShIklqGgiSpZShIcyjJY5J8L8l+Se7fPB/g4UPXJXXlzWvSHEvyVmA/YH9Gcxa9beCSpM4MBWmONVNRfBv4HfCEqto6cElSZ54+kubeIcADgAMY9RikPYY9BWmOJVnNaCrvI4DFVfXygUuSOpu4WVKlPiX5W2BLVX2seR74fyV5alV9dejapC7sKUiSWo4pSJJahoIkqWUoSJJahoIkqWUoSJJahoIkqWUoSJJa/wdDYuZxhUxAzgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "k = 1 # shape parameter\n", "weibull = np.random.weibull(k, 1000)\n", "N = 10 # slice to show\n", "print ('First', N , 'Weibull samples:\\n', weibull[:N])\n", "print ('\\nMean of Weibull samples:', np.mean(weibull))\n", "plt.hist(weibull, 25)\n", "plt.rcParams[\"font.size\"] = \"15\"\n", "plt.ylabel('Fraction of samples')\n", "plt.xlabel('x')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Empirical histogram and theoretical distribution function\n", "Let's draw together a empirical histogram and theoretical Weibull distribution function." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Weibull mean: 1.0 \n", "Weibull variance: 1.0 \n", "\n", "Random Weibull variates, first 10 :\n", " [0.34948416 2.74203849 0.77025574 2.38311747 0.77147725 0.353662\n", " 2.69172559 0.76665722 0.56800008 1.0336529 ]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "shape = 1\n", "from scipy.stats import weibull_min\n", "mean, var, skew, kurt = weibull_min.stats(shape, moments='mvsk')\n", "# var -> variance = σ^2 (sigma square)\n", "print('Weibull mean:', mean, '\\nWeibull variance:', var, '\\n')\n", "\n", "x = np.linspace(weibull_min.ppf(0.01, shape), \n", " weibull_min.ppf(0.99, shape), 100)\n", "# ppf - Percent point function (inverse of cdf — percentiles).\n", "\n", "ax.plot(x, weibull_min.pdf(x, shape),\n", " 'r-', lw=5, alpha=0.6, label='Weibull_min PDF')\n", "\n", "# Frozen PDF\n", "rv = weibull_min(shape) \n", "ax.plot(x, rv.pdf(x), 'k-', lw=2, label='Frozen PDF')\n", "\n", "# Samples of Weibull variates (empirical)\n", "r_weibull = weibull_min.rvs(shape, size=1000)\n", "print('Random Weibull variates, first',N,':\\n', r_weibull[:N]) \n", "ax.hist(r_weibull, density=True, histtype='stepfilled', alpha=1.8)\n", "ax.legend(loc='best', frameon=False)\n", "plt.ylabel('Fraction of samples, normalized')\n", "plt.xlabel('Weibull variates')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Estimation of the sample averages " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will estimate the distribution of the sample averages of a random Weibull variates for different sample sizes. To do this, we take three **N** (5, 10, 50), **generate 1000 samples of volume N each** and plot histograms of the distributions of their sample averages. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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7pQbg3vMxuCYbJ6lq5I/CUIzn4y7zR1ORDjf/xLVv/ZtE6RxXGq+GOzXO2Qu0nG1Wy7AB95lrGyWuBrgfARMjp0WKN+mZhDuRHIU7sAtwQ6uETPTWNQzXCHOaqoYOmAW4A7O+ltHQPw59cJcTwoWy//A3fz3RG/VWS22fqq4Gngee9w7kV4FzROQhVf0Bl4wkA8NVdc+vNu/yd7Rf3lWpDzA9oizaPosUaji8rRLv22m4E95vVHV8+ATvsug+1dCqWigirwN/EpEuuI4VQskvnflAD+A7rURDV++y8MnAq6p6RcS0yMb2+bgTec8oq+oVpWw+rhPJsmiXiSN5X2ATvAfieulNBW7FfVlWK+9y+b+Af4mrProX15HiFFznotKExnrqS8lxn/p4f0PHWuj470nJ4y/avi2Nn5+ruFTD+3oe3rk4PPEVkWjHYEifUspC70FVnqd3A6Fk9BkRqaeqT0bM057SO9pE6oy79Fvt4vgslOu8VsXi/Q6MFDqfF1X2/VXVybgfGaFLrz8Bd+LaeZbmUdyP3qtUNVrTjFCMa6vgGNxDVYtE5GYvvr+Uc/FHcR2y4vEyrj1ilVDVYhH5EThARBpEVHQchPtBN6Ws9cR1WzNv5ZNwjSVPxrVrCf91/wvu0tAoXDXshLBl1+FqaEZIWDfrEK9NQ7y/6K70MuvQsk1xVbAb2TejnQccKmFj+4lIc8J6klUFEWkkEeMHeif1UFIVSjRDv9Qif3HdQvXfWu46cQMqugBE2uG+HOeWkXx8jEtsbhKREgmzuLHKyhprLurrFjc8SXbJ2YG9Cd35uC+0ueFtqDyv4PbbPUQhIvFW6ceKrzWuh+Ye3vs6Fjdm5OHs6/oo637V+3u3l/hHxpgV9n+0u8LMwf2YKk8PxHILtesKL/PaB/3kPQ3f/tYY8byHSxBGhbd78fbjhbiG4aH1ve/9/ZO43mOhefvjagfKw8/PVZmq6X0NdU4J33eCSxpjOU5EDoyY/wbv6f+gys/TqOuleSauJ+kTIvKniFkC1yavHJ+FipzXqkq834GRfsJ9T1/h/YDeh7ihXEo9JmMczytwV1XKWvZa4A+4trhPxZjtTVyCfJuIlKg9E9fmNtaly1Kp6v+Ab3E1euUZDsjPNnkA/8a1u7ssovxa3BWnyHbYJZTn8uV4XE3eYUSMtKyqKiJfsXc0/PH7LsqVuMadX4rIK7gDLglXs3YK7ks7J44Y1gLfi8g/cR+wC4EOwCURl3Mex/0S+0JEXsU1yL8U92VTlR/CHsBEEXkH9wHagPtVdSXuV2qoAe07uEt/H4nIs7hBGo/DNYQt7x1ByisFd6nh37h2bFfgqp+vKW0hVd0mIufjvgTmevt8AW5f9sL9Uj+N0ge8Hou7TPqqiDyO2z+H4y6FLCTK8aeqP4nIDNz+Ssd9YUfO8x8ReRF3WfxAXBuPtbiew4fiOhqUWWurqltE5BPgXHFj5/2A6yRwOe79i2wTcysuERnnvZ4VuNqY0JffnkspqvqDiIzGtX+ZJiJv4S5vt8b9WDoR17MT4Dkv+f4Ed4ym4sY/SsN9NqpTGrBaRN7DfS7zcbUmV+Ler/fD5v0OOFbcuHLLcB/9N1R1rrhxxG7AfcbHsHcIlSbA70KX2lR1pvcZuAz4zPvsZOK+AH7C7Zt4Li+CT58rceMDLlXVTmXMWh3v639w7Va/8M6l9XDn3dIaYP/szf8E7jLYKbjLkK9GXDKuqvM0sKdm/hxczd7fRSRFVR/yplWqTZ6InIf7rII7fuqLSCjRXaqqr4bNewGuA9ltqlpa/PF+Fsp9XqtC8X4H7sP7jj4P12Z8urf8TNxx0w13Pr8Z11EqlltF5Hj2DjcluOF5elFKgiOuE8tDuET9RxE5N2KWhao6SVVXiMiVuKtis73v7qW497c/7jjvQ8VrdG/EfSf3xl2VKVN1tMkTkSNxl7rB9VwH91220dvmnWGzP4d7jx8W14xgNu44Ow24M/wKRkwaf1ffI9jbVXholOnXetMKCeviHTa9JW7cuHm4yw0bceNHPQr0CZvvAkoO8RAqOxb3pbkMl/H/Avw2RryjcAfITm/HXFTGusPLhhFfl/IMXBubad7rKcAlQn8HWkfMeyruMs023Af1DdyHcwlhQ5fo3i7gL0XZ3kt4Py4jykvEy94hVPriGpvmevt9Mq7Ba+Q6SsThlffDJcwrcV+iebhfRH8DWsRx3ByJ++LY4u2jD711TiDGsAe4mjHF/WJuX8q6z8N9aDd7r20JbiTws8Lm6eStKyfGOlriTiqrvHXMwP0gKHFcePPvj/ty2o5rFvAK7otAiTKUDi4J/NibdyeuDdVY4MqweUbgasNWePOswf0qPz3Oz2as9y7acbHP68Ilmvd4x8U6b/tLcO1YukesrzsuYdnsrUMjpl+K+3Lc4c3zKTAkSlzJuB+Koc/xdFytz4PeerPC5n0pcjs+f67SvLJv4nhf4npfS3uN0WL29vMsbz+vxrUnbRE5L2HHPq7pw/SwY/B2woYHivg8lHmeLuU1T6Dk0B1J7B2K4uZ4juk4t6MxHpHv+x+98kvLWGd5Pgtxn9eiHYteeQ5Rhs8gyjmLcn4HRovDK++I6427BHc+X4f7/NxDKefasM/DGG/ZAtw57XvcVQ+JEuuwsOVivVfRju/DcT/g8r0YV+Eqjq7HG26ljDgVbwiVKNPe9abHNYRKdTzC3veojyjzN8NVXK3y3vNZuHEaJZ7thcYSMwlGXI+i0UBnLTl8galC4gYZnYL7ArvX73hqKxF5HzfobLrWQCP7ihCR3+C+KI5R1S/Kmt9P3i//xZRdg5XQROS/uJqgPlrKYL9BFlYbeZSqTvA3GlOb+N5uxZjaJLKtSET7pk9LLmEixWhvMwDXKPuLoCZ4nhNwtQSBTvCMI258wqOBm2prgmdMZdhNvo0pn2ki8gXuElZjXJuUIbhRyaf6Glnt8XuvveeHuEuYvXBt9HbhhmoKLFX9g98xmPipu0doM7/jMMYvluQZUz7v4hK783Cfn8W49on3+RlULfMjruHwNbi2ZFtwDcJvU9Wf/AzMGGMSibXJM8YYY4xJQFaTZ6pcy5YttVOnTn6HYYwxtcrUqVPXqmp57gRiTKksyTNVrlOnTkyZUuZA3MYYY8KISFz3gDUmXta71hhjjDEmAVmSZ4wxxhiTgCzJM8YYY4xJQJbkGWOMMcYkIEvyjDHGGGMSkCV5xhhjjDEJyIZQMcbUaps3byY/P5/du+3WpCa46tWrR1ZWFunp6X6HYuoQS/KMMbXW5s2bycvLo23btqSmpiIifodkTAmqSkFBAStXrgSwRM/UGLtca4yptfLz82nbti2NGjWyBM8ElojQqFEj2rZtS35+vt/hmDrEavKMqWqVTTbsftJx2717N6mpqX6HYUxcUlNTrVmBqVFWk2eMqdWsBs/UFnasmppmSZ4xxhhjTAKyJM8YY4wxJgFZkmeMMT7KyclBRPY82rRpw+mnn87ChQujzpOUlETz5s0ZPHgwf/3rX8nNzS2xzvD1hT++/vrrSsf73HPP0blzZ1JSUhg2bFjUeSZMmICI0LJlS7Zu3brPtMcffzzqZcu3336bbt26UVRUBMCuXbsYNWoUQ4YMqZKe05s2beLCCy+kefPmNG3alN/97nesW7euzOWefPJJTjrpJDIyMhARJkyYUGKeP/zhD1x88cWVis+Y6mBJnjEB8vKBJ/Obx79m9Lu/8OH01azftsvvkEwNaNq0KZMmTWLSpEk8+OCDTJs2jWOOOYZt27aVmOfbb7/ljTfeYMSIEbz66qv079+fqVOnlljn9ddfv2edocd+++1XqThzc3O58sorOeWUU5g4cSJPPvlkqfOvW7eOp556qsz1FhcXM3r0aEaNGkVycjIA27dv5/nnn6dRo0YcdthhlYob4KyzzmLChAk8//zzvPTSS/zwww+ceuqpZS73yiuvsH79ek444YSY84waNYrXXnuNBQsWVDpOY6qUqtrDHlX6GDhwoNZprn9suR8f9jxcO974gR55/xfa69ax2vHGD7Tf6HG6bN02v19RYM2aNcvvECpt9OjRmpGRsU/ZV199pYC++eabMedRVd2wYYP2799fu3btqoWFhXvKAX3ssceqPNZQXD///HOp840fP14BHTZsmLZq1UoLCgr2THvsscfUffXs9cknn2jDhg118+bN+5QXFxfHXKY8vv32WwV04sSJe8q+//57BfTTTz8tddmioiJVVZ0xY4YCOn78+KjzHXPMMfrnP/+5zFhKO2aBKRqAc7g9EudhNXnGBMDUNr247qQ/M3DFLD6+9kim5xzPmMsOoahYue39mX6HZ2rYwIEDAViyZEmp8zVr1oz777+fhQsX8umnn1Z6u48//jjdu3enQYMGdOvWjUceeWTPtJycHIYMGQLAfvvth4jw0ksvlbq+G264gQ0bNvD888+XOt/LL7/M8ccfT1pa2j7lVdUbdezYsbRq1YojjzxyT9lBBx1E586dGTt2bKnLJiXF9zV5+umn89prr1FcXFypWI2pSpbkGeOzpc2yufT0v5G9dR3P/fdOGtZLpl5yEgd3yeDaY7vz2ex8PplZst2VSVyh5C47O7vMeY866ihSUlL47rvv9ikvLi6msLBwzyPU1i2W5557jj/+8Y/85je/4f3332fkyJFcf/313HvvvQBccsklPPHEEwC89tprTJo0iZNOOqnUdbZv357zzz+f+++/v9Tx4b744osquSQby5w5c+jVq1eJ8t69ezNnzpwq2cZhhx1GXl4eM2bMqJL1GVMVbDBkY3x22zGXUZiUzItv5dCiYPM+0y48vDP//XElOe/N5PBuLWncwD6yZbnt/ZnMWrW57BmrQZ826Yz+dd8KLVtYWAjAokWLuOqqq0hLS+PYY48tc7kGDRrQsmVL8vLy9in/05/+xJ/+9Kc9zw8//PCYHS+Ki4vJycnhggsu4KGHHgLg+OOPZ9OmTdxzzz1ce+21tGvXjj59+gAwYMAA+vXrF9fruummm3jxxRd55ZVXonZOWLVqFatXr457fRWxYcMGmjVrVqK8efPmLFq0qEq20bdvX5KTk5k8eXKl2z4aU1WsJi/BiUg3EXlGRH4WkSIRmRDHMoNF5EURWSAi20VkroiMFpGGNRBynbIiPZPxXQfx+x8/oMuGVSWm10tO4s5T+7Fq0w4e/Xy+DxGamrBu3Trq1atHvXr16NmzJ4sWLWLMmDG0bt06ruVVS94lZdSoUfzwww97Hi+88ELM5VesWMGqVasYOXLkPuVnnXUWmzdvrlTtVNeuXTn77LO59957o9YmhnoHt2zZssLbiEe0S7+qWmWXhFNSUmjWrFnU3s7G+MWqBRJfX+BE4DugfpzLnAV0Be4D5gMDgDu8v6dXQ4x11pj9XI+9s37+OOY8gzq14OzB7Xnh68VceHgnWje123iVpqI1aX5q2rQpn332GSJCdnY2bdq0iTv52LFjB+vWraNVq1b7lHfo0IFBgwbFtY7Vq1cDlFhH6Pn69evjWk8st9xyC/369WPMmDElpu3YsQNwNZLVpXnz5qxZs6ZE+caNG6PW8FVUgwYN9rweY4LAavIS3/uq2l5VRwLxtuC/T1WPVNXnVHWCqv4DGAWMEJGO1Rdq3bI7KZk3BhzPsEVTabe55BdQuMuHdqWoWPng59U1FJ2pSSkpKQwaNIiBAwfStm3bctUujR8/nsLCQg499NAKbz9UY5ifn79PeegScIsWLSq8boA+ffpw2mmncffdd5eodQyte+PGjZXaRml69eoVte1drLZ6FbVx48ZK7ytjqpIleQlOVcvd1UtVo2UcP3l/syoXkQn5vNtBrGnSgt9OK713H0Dnlo3p37Yp708veUnX1F0bN27kxhtvpFu3bnG134ulXbt2tGnThrfeemuf8jfffJP09HT69+9f2VC59dZbmTlzJu+8884+5Z07d6Z+/fosXry40tuIZfjw4eTm5u7TJnHKlCksWrSI4cOHV8k21qxZw/bt2+nRo0eVrM+YqmCXa028DgOKgbl+B5IoXtt/OK03r+GohVPimv83+7Xhro9ms2TtNjq1bFzN0ZmgKSws3NODdsuWLUydOpWnnnqK7du3M27cuD2DCFdEUlISOTk5XH755WRkZHDccccxceJEnnrqKe6++24aNqx8c9wDDjiA4cOHlxiypEGDBgwcOJCpU6dy4YUX7jNt7NixbNu2jWnTpgHwn//8B4DBgwfTsaO7qJCTk8Ntt90WtV1iyKGHHsoJJ5zA+eefz4MPPkhSUhI33ngjRxxxxD7J8cUXX8zEiRP3GdR4ypQpLFmyhOXLlwMwceJE1q5dS6dOnfa5HD5lyhREpFp7CRtTXpbkmTKJSDbwV+BVVY3abVFELgMuA9cWyJRuabNsvup8INd+/RopcVa2njSgNXd9NJsPpq/i6qO7V3OEJmg2bdrEoYceioiQnp5Ot27dOPfcc/njH/8Y11ArZbn00kvZuXMnf//733n00Udp164dDz30ENddd10VRO/ceuutUcelGzFiBE8//XSJ8iuvvJKlS5fueR7qGPLiiy9ywQUXAO7OGJmZmWVu+4033uC6667joosuori4mJNPPpl//OMf+8xTVFS0p5dzyOOPP87LL7+853lOTg4Av//97/cZJ3DcuHEMHTqUjIyMMmMxpqZIab9+TGIRkf8ALVV1WDmWqQ98BrQDBqrqhrKWGTRokE6ZEl/tVEKKoz3VfUf+nmcOHsE3T19E6y0R988s5TM58ulv2VxQyMfXHRlznrpk9uzZ9O7d2+8wTCXl5eXRoUMHvv76awYPHlyuZYcOHcrRRx/N6NGjqym6shUVFdGxY0fuvfdezj333FLnLe2YFZGpqhpfbxlj4mBt8kxM4lp/v4LXQzeeBM/E5+Meh3D40p9LJnhl+PV+bZibt4W5uVuqKTJjal6rVq245JJLePTRR8u1XGFhIb/88gtXXXVVNUUWn7feeovU1FTOPvtsX+MwJpIleaY0jwCnAKeoatUMC29YkZ7Jooz2DF1U8qbyZRnerzVJAu//bB0wTGL529/+Ru/evcu8M0e4lJQU1q1bF9fl2uqkqrzwwgukpFgLKBMsluSZqETkZuCPwLmqGn2YfFMhX3U+EIChi38s97KZaQ04vFtL3p++qtSG5sbUNtnZ2fz1r3+tVAcSv5xzzjn73BfXmKCwJC/BiUgjETlDRM4A2gKZoeci0sibZ4GIvBC2zG+Bu3GXaleKyCFhD39/MieArzodQPaWtXRbt7xCy588oDVL121n1mp/bt1ljDGmdrC65cSXBbwVURZ63hlYgjsOwn8+H+/9vcB7hLsQeKkK46tTiiSJrzvtzwnzJlHRmykN6e7y7O8Wradvm6ZVF5wxxpiEYjV5CU5Vl6iqxHgs8ebppKoXhC1zQSnLvOTTS0kI07O7sblhE4Ys+ansmWNo0yyVjhmN+G5R+TptGGOMqVssyTOmBn3V+UBEizliybRKreeQzhlMXrye4mJrl2eMMSY6S/KMqUFfdTqA/rkLaFFQufZ0h3RtwaaC3czOtXZ5xhhjorMkz5gasqV+Kj+27cWQxRW/VBtycGc3qv53i9ZXel3GGGMSkyV5tYiI9BKRU0Wkjd+xmPL7tuN+FCUlV6o9Xoi1y0scOTk5iAgnnHBCiWlnnHEGw4YNq5E47rjjDo499ljS09MREZYsWRJ1vm+++YaDDz6Y1NRUOnfuXOLWYMaY4LAkL6BE5BkReTrs+VnADOC/wBwRsbtg1zJfdTqARrsKOHBl1Ywrbe3ySiHiz6MSPvnkE3744Ycq2gHl98wzz1BYWMhRRx0Vc54FCxZwwgkn0LlzZz788EMuv/xy/vznP/P888/XYKTGmHhZkhdcvwK+DHt+B/BvoA3wsffc1CLfdejPwct/oX5xYdkzx8Ha5SWOFi1aMGDAAO666y7fYli2bBkTJkzg0ksvjTnPAw88QJs2bfjXv/7F0UcfzU033cRll13GbbfdZoNzGxNAluQFVxawHEBEugPdgPtVNRd4FjjAx9hMOW1q0JgFLTtUWS0eWLu8RCIi3HLLLbz33nvMmDHDlxiSksr+Ohg7diwjRozY5/ZdZ599NitWrOCXX36pzvCMMRVgSV5wrQdaef8fC+SqaugsKuw7eLEJuOmtuwNwwKqqS/KsXV5iGTlyJD169Ch3bZ6qUlhYWOajsrZt28by5cvp1avXPuW9e/cGYM4cu721MUFjSV5wjQVuF5E/ADcBb4ZN64e7U4WpJX5q0wvRYgasnl+l67V2eYkjKSmJm266ibfeeot58+bFvdzLL79MvXr1ynxU1saNGwFo1qzZPuXNmzcHYMOGDZXehjGmatltzYLreuAR4Apc27zRYdNOA8b5EZSpmJ/a9KTbuuWk79pepes9pGsLxkxZzuzczXaLswRw7rnnctttt3HPPffw4osvxrXMr3/96xrtsCExOpjEKjfG+MeSvIBS1U3ARTGmDanhcEwlKDCtdQ+OW/B9la97YIcWAExbvtGSvASQkpLCDTfcwDXXXENOTk5cy7Ro0YKmTav/vQ/V4IVq9EJCNXiRNXzGGP/Z5dqAE5E+InKeiNwiItleWTcRSfM7NhOfpc1as6FRUw5YNbfK192+RSrNGtVj+vJNVb5u44+LLrqIrKws7rvvvrjmr6nLtY0bN6Z9+/Yl2t6Fnke21TPG+M9q8gJKRJoA/wTOAHbj3qtxQC5wN7AM+ItvAZq4/dSmJwD7V0OSJyL0b9uU6SstyUsUDRo04C9/+Qs333wzAwcOLDNBq8nLtcOHD+edd97hzjvvJDnZ9f0aM2YM7du3p1+/fjUSgzEmfpbkBdfDwGHAMcA3wI6waR/hEjxL8mqBn9r0otGuAnqsXVYt69+vXTOemriQgl1FpNa3TteJ4PLLL+fuu+/m22+/ZejQoaXOm5GRQUZGRqW3OXHiRNasWcPUqVMBN1xKZmYmffr0oU+fPgCMGjWK1157jfPOO49LL72UH374gWeeeYannnrK2uQZE0B2uTa4RgA3qup4oChi2lKgY82HZCpiWpse7Ld6HslaXC3r79+uKUXFyqzVNijyHqr+PKpIo0aNuO6666psffEYPXo0I0eO5N577wXgqquuYuTIkbz55t6O/d26dWPcuHEsWLCA4cOH8+STT/LQQw9xySWX1Gisxpj4WE1ecKUCsQZAS6Nk4mcCaEdKfWZldeHSye9U2zb2a9cMgOkrNjKwY/Nq246pHjk5OVE7Wdxyyy3ccsstNRbHhAkT4prviCOOYPLkydUbjDGmSlhNXnD9AJwfY9oZwLc1GIupoF9adaUwOaVKB0GOlN20IVlpDZi+wtrlGWOM2ctq8oLrVuAzEfkMeAs3EseJInIdLsk70s/gTHx+auN6HO6/uuo7XYQb0K4p01dsrNZtGGOMqV2sJi+gVPVrXKeLBsDjuFuZ3QZ0AY5V1Zob/dRU2LQ2PWi7KY+sbRurdTsD2jVj0dptbNmxu1q3Y4wxpvawJC/AVPUbb+DjdKAdkKaqh6vqN/GuwxtT7xkR+VlEikRkQpzLNRWRF0Vkg4hsEpHXRKTyXfjqmGmte1TL0CmRBrRriirMsKFUjDHGeCzJqwVUtUBVV6lqRe6J1Rc4EZjnPeI1BhgGXAJcAAwG/leB7ddZGxs2YWXTVvTLW1jt2xrgdb6YUQfb5WkV9mo1pjrZsWpqmrXJCxARub8cs6uq3hjHfO+r6rve+v8DtIwjjkOBE4ChqvqlV7YS+F5EjlXVz8oRZ501K6szAH3yF5dvwQqMN9YCaHf580x/5CsYem+5l6+t6tWrR0FBAY0aNfI7FGPKVFBQUCV3HzEmXpbkBcvIcsyrQJlJnmqFBmcbDuSFEjxvPZNFZLE3zZK8OMxq1RWAPnmLamR7++XOZ3p29xrZVlBkZWWxcuVK2rZtS2pqqg3IawJJVSkoKGDlypW0atXK73BMHWJJXoCoame/Y/D0AqKN+THbm2biMCurC1lb1pG5fWONbK//6gV82GsI67ftokXj+jWyTb+lp6cDsGrVKnbvtk4nJrjq1atHq1at9hyzxtQES/JMNM2BjVHKN+B695YgIpcBlwF06NCh2gKrTWa26kLf/JqpxQMYkOuaXE5fsZFhPbNqbLt+S09Pty9OY4yJwjpeBJiIZInI3SLymYjM9P7eJSI1Ud8frYWwxChHVZ9V1UGqOigzM7N6I6sFdiTXY0FG+xq7VAvQ19uW3d7MGGMMWJIXWCJyODAfuBxYC3zu/b0CmO9Nry4bgGZRypsRvYbPRJiX2ZGipOQarclrunMbbTflM3v1lhrbpjHGmOCyy7XB9TgwFfi1qm4LFYpIE+AD4DHgwGra9hxgSJTyXtgwKnGZleWuatdkTR5A7/zFzF4d9Yq6McaYOsZq8oKrF/BQeIIHoKpbgQeB3tW47bFAtogcESoQkUG49nhjq3G7CWNmqy402bmdDhtza3S7vdcsZtGarezYXVSj2zXGGBM8luQF1ywgO8a01kTv/VqCiDQSkTNE5AygLZAZei4ijbx5FojIC6FlVHUS8DHwioiMEJFTgdeAr22MvPjMyupC7/zFJEVvwlhteucvplhhft7WGt2uMcaY4LHLtcH1R+BVEdkK/E9Vd4pIA+A04Cbg/DjXkwW8FVEWet4ZWII7DpIj5jkbeAT4J+7HwAfANeV8DXVSkSQxO6szZ07/tMa33dsbeHn26s30b9e0xrdvjDEmOCzJC653gUbA6wBestfEm7YDeCd84FdVjTpmhqouwfWKjUlVO0Up2whc6D1MOSxtls32+qnlv9NFFei4YTWN6idbD1tjjDGW5AXYE8QYrsQE28w9d7qo/nvWRkpC6ZmdxmxL8owxps6zJC+gVDXH7xhMxczK6kJKUSHd1y3zZfu9W6fzwc+rUFW7zZcxxtRh1vHCmCo2s1UXuq9dRoOiQl+237t1Opt3FLJq0w5ftm+MMSYYrCYvwETkTFxHi7ZAw8jpqnpQjQdlyjQrqwtDF0/1bft9WqcBMHvVZto2S/UtDmOMMf6yJC+gRORe4AbgB2ABsMvfiEw81m3dydomzem9ZolvMfTMdvdxnb16M8f2qYk74BljjAkiS/KC6yLgr6p6j9+BmPjNzXW3FOvpY5LXpEEKHTMaMTvXOl8YY0xdZm3ygms37rZmphaZE4AkD6B3drrdw9YYY+o4S/KC61HgErHukbXK3NwttNi+icxtG32No3frdJas28b2Xf50/jDGGOM/u1wbUKp6v4g8CMwRkYnAxpKz6I01H5kpzZy8LfRcs6T00adrQO/Waai6msUDOzT3ORpjjDF+sCQvoETkd8C1QDHuTheRHS8UsCQvQIqLlfl5WzhzzVK/Q6F3672dLyzJM8aYusmSvOC6FxgDXKGq1riqFli+YTvbdxXRy+f2eADtmqfSuH4y83Lt0DHGmLrK2uQFVzrwT0vwao9Qp4sgJHkiQo/stD0xGWOMqXssyQuut4Gj/A7CxG9u7hZEoMda/y/XAvTKTmNe3hZU7RbIxhhTF9nl2uD6GLhXRLKBLyjZ8QJV/aimgzKxzc3dQocWjWi0e6ffoQDQo1Ua/568nDVbd5KVVuKGKcYYYxKcJXnB9W/v70XeI5ICyTUXjinLnNzN9GyV5ncYe/TMdrHMzd1iSZ4xxtRBluQFV2e/AzDx27G7iCXrtnNS/9Z+h7JHKOGcm7uFId0zfY7GGGNMTbMkL6BUNRgNu0xcFuRvpahY99w3NggymjSgZZMGe261Zowxpm6xJC/gRCQF6ACUuN6mqrNqPiITzZ571mYH53ItQM/sJszLsyTPGGPqIkvyAkpE6gH/AH4PNIgxm7XJC4i5eVuon5JEp4xGfoeyj56t0vn35GUUFytJSX7fh8MYY0xNsiFUguv/gJOBiwEBrgYuBD4HlgC/jndFItJHRD4Xke0iskpEbheRMhNEERkkIp+IyDoRWS8in4nIwRV6NQluTu4Wumc1ISU5WB+pntlNKNhdxPIN2/0OxRhjTA0L1jeSCXcmkAO86T2frKqvqOrxwNfAKfGsRESaA5/heuOeAtwOXA/cVsZy7b3lUoDzgfO8/z8RkY7lfTGJbm7u5sBdqgU3jApg7fKMMaYOsiQvuNoD81S1CNgBhN+A9DXg9DjXcwWQCoxQ1U9V9WlcgvdnESmtl8BJQJq33Ieq+iFwGu4+uieW76Ukto3bd5G3eWeghk8JsSTPGGPqLkvygms10Mz7fzFwZNi0ruVYz3DgY1XdHFb2Bi7xG1rKcvWAQmBrWNlWr8wad4WZl+d2URBr8ho3SKF9i1TmWucLY4ypcyzJC64JwBDv/+eAW0TkdRF5EXgIeDfO9fQC5oQXqOoyYLs3LZa3vXkeEpEsEckCHgE2AG/F+yLqglACFcQkD1znC6vJM8aYusd61wbXX4GWAKr6dxER4AxcDdxjuLZ18WhOlFui4ZK15lHK8ba5SkSOAj4ArvGKVwMnqOqayPlF5DLgMoAOHTrEGVpimJe7hbSGKWSnB/OuEj2zmzBhbj47C4tokGIdso0xpq6wmryAUtVcVf0l7Pkjqnq4qh6oqjeq6rbyrC5KmcQodxNFWgP/AabiLvkO9/7/UERKZHGq+qyqDlLVQZmZdevuCnPzttCzVRouDw+entnpFBYri9aU55AxxhhT21mSF1AikiIiDSLKjheRa0XkgHKsagN72/aFa0r0Gr6QUbia3jNUdZyqjsN19igC/lKO7Sc0VWVe3hZ6BPRSLey9vZkNimyMMXWLJXnBNQZ4KvRERK4BxgH3AN+LyMlxrmcOEW3vvOFRGhPRVi9CL2Cmqu4OFajqLmAm5ev4kdDyt+xk4/bdgexZG9IlszH1koU51i7PGGPqFEvygusQ4KOw56OAh1Q1FXge12YvHmOBE0QkPAs5CygAJpay3FKgn4jUDxV4NYv9cIMxG/YOTdIjwEleveQkurRswnyryTPGmDrFkrzgygByAUSkP9AGeNqb9hbQJ871PA3sBP4rIsd6HSRygIfDh1URkQUi8kLYcs9723xHRE7yag7/B7QGnq3oi0o0oUugPVo18TmS0vXITrOaPGOMqWMsyQuuPKCT9/+vgKWqutB7ngoUx7MSVd0AHIO7z+37uIGQHwFGR8yaQti9cFV1qrfdNOBV4BWgEXCcqv5c/peTmObmbqFlkwZkNIl1e+Fg6NmqCSs2FLB1Z6HfoRhjjKkhNoRKcL0F3Cci++HuWft42LQDgPnxrkhVZwFHlzFPpyhln+PulWtimJe3hZ7Zwa7Fg72Xk+fnbeGADjFHzjHGGJNArCYvuG4CnsF1gHgKuDts2kBcxwzjo+JiZV7e1kC3xwsJDdRsPWyNMabusJq8gFLVQmIMeKyqI2o4HBPFig0FFOwuCnTP2pD2zRuRWi+Zublby57ZGGNMQrCaPGMqKOi3MwuXlCT0aNXEavKMMaYOsSTPmAoKJUzda0FNHrh2eXMtyTPGmDrDkjxjKmhu7hbaNU+lSYPa0eqhZ3Yaa7bsZP22XX6HYowxpgZYkmdMBc3z7llbW4Q6iMy18fKMMaZOsCQvQERkkTdkCiLyfyLSxu+Y6hyRuB67k1NYuHI9PV58ouT0gLIetsYYU7dYkhcsbXEDDoMbrLidj7GYUixu0ZbdyfXosXap36HELSutAU1T61m7PGOMqSNqR2OiumMhcLWIZAACHCYiLWPNrKofxZpmqteczE4A9FxTe5I8EaFndhrz7HKtMcbUCZbkBcvNwMvAOYACD5cyrxJ2GzJTs+a27EhycRFd1y/3O5Ry6dkqjf9NW4mqIgG+tGyMMabyLMkLEFV9V0RaAG2AZcAI4Cd/ozLRzM3sRJf1K2hQVLvuBdsjO40tOwrJ3byD1k1T/Q7HGGNMNbIkL2BUtRhYISIXAl+p6jq/YzIlzcnsyP6r5/kdRrmFegPPyd1iSZ4xxiQ463gRUKr6sqquE5E2InK6iFzq/bUetz7bWj+VFc2y6bVmid+hlFuPVk0AG0bFGGPqAqvJCygRSQIeBy5l37Z3RSLyLPBHr9bP1LC5LTsC0LMWJnnNGtUnO72hdb4wxpg6wGrygut24CLgFqATkOr9vcUrz/EprjpvbqZL8nrVop614XpmpzHHkjxjjEl4luQF1/nArar6gKouU9Wd3t8HgL8BF/gbXt01N7MTjXdup+2mfL9DqZBerdNYkL+V3UVWEWyMMYnMkrzgygKmx5g23ZtufDAnsxM91i4jCfU7lArpnZ3OrqJiFq/d5ncoxhhjqpElecE1Dzg7xrSzgbk1GIvxKO5ybW3sdBESur3Z7NWbfY7EGGNMdbKOF8F1J/CGiHQA/gPk4WrvRgJHETsBNNUov0kLNqam18pOFyFdM5uQkiTWw9YYYxKc1eQFlKq+CfwKaAw8CrwN/AN3b9tfqepb8a5LRPqIyOcisl1EVonI7SIS190yRGSEiPwgIgUisk5ExolI4wq8pIRQG29nFql+ShLdsppY5wtjjElwVpMXYKr6CfCJN5xKS2BteYdNEZHmwGfALOAUoCvwEC7Bv7WMZS/BDeNyPzAKaA4cTR0+bvb2rF3ibyCV1DM7jR8Wr/c7DGOMMdWozn5Z1yZeYlfRrpxX4IZfGaGqm4FPRSQdyBGR+72yEkSkJfAIbjy+58ImvVPBOBLCnJadyNqyjuY7anctWK/sdN6dtopNBbtpmlrP73CMMcZUA7tcm/iGAx9HJHNv4BK/oaUsd6b39+XqCqw2mpfZkZ5ra++l2pBerV3nC2uXZ4wxicuSvMTXC5gTXqCqy4Dt3rRYDsb14L1YRFaIyG4R+V5EDqu+UIOtSJKYn9G+1l+qBeiVHbqHrfWwNcaYRGVJXuJrDmyMUr7BmxZLNtAT127vRuDXwDZgnIi0ipxZRC4TkSkiMmXNmjWVDjqIFjdvw856DehRiztdhGSnN6Rpaj1mr7aaPGOMSVSW5NUN0UbtlRjlIUlAE+BiVX1NVccBpwJFwNUlNqD6rKoOUtVBmZmZVRBy8MzO6gxAn/xFPkdSeSJCr+w05lpNnjHGJCxL8hLfBqBZlPKmRK/hCwl1vZwQKvDa9U0F+lRNaLXLrKwu1CvaTfe1y/0OpUq4JG8LxcW1884dxhhjSme9awNKROoBfwJGAO2AhpHzqGo8tzabQ0TbOxFpjxt/b07UJZzZuJo+iQwNqJM3PZ2d1Zmu61ZQv7jQ71CqRK/W6WzbVcSKDQV0yGjkdzjGGGOqmCV5wfUIcDnwATAe2FXB9YwFRolImqqGGmCdBRQAE0tZ7gNgNO7uGh8BiEhTYCDwYAVjqdVmZXXmiCXT/A6jyoR3vrAkzxhjEo8lecE1ErhJVR+q5HqeBq4B/isi9wFdgBzg4fBhVURkATBRVS8GUNUpIvIu8IKI3ASsBW4AdgNPVDKmWmdto6bkp2UkRHu8kB6tQkneFo7vm+1zNMYYY6qatckLLgGmV3YlqroBOAZIBt4HbsPVEo6OmDXFmyfcucD/gIdx98/dDRztrbNO2dvpYrHPkVSdxg1S6JjRiNmrrfOFMcYkIqvJC67ngHOATyu7IlWdhbsdWWnzdIpSthW40nvUabOyugDQO4GSPIC+bdL5ZaUlecYYk4gsyQuuPOB3IjIel+htjJiuqvpUjUdVR83K6kKbzfm1/nZmkfq2acpHM3LZvGM36Q3t9mbGGJNILMkLrr97fzsQ/fZjCliSV0NmZ3Wmd/4Sv8Oocn3apAMwa9VmDumS4XM0xhhjqpK1yQsoVU0q4xHZfs5Ukx0p9VmY0a72dLoQifvRd2BPAGaeddG+04wxxtR6luQZU4Z5LTtQlJRMn7xakuSVQ9a2jWRuXc/MrK5+h2KMMaaK2eXaABORZrix8o4AWuDuQvEV8KyqbvQvsrol1LM20TpdhPTNW8SsVl38DsMYY0wVs5q8gBKRrsAM4Hbc3SmWeX9vB6Z7000NmJXVhcY7t9NhY67foVSLfnkLmN+yAzuSreOFMcYkEkvygusRXI/aLqp6tKqeo6pHA1298od9jK1OmZXVhd5rFpNEYt7jtW/eIoqSkpmX2dHvUIwxxlQhS/KCaxjwf6q6MrzQe34b7nZjppoVI17P2sS8VAvQN28hADNbWeWwMcYkEkvygkspeQeKkCRvuqlmK5pmsbVBo4S600Wk9pvySNuxlV8syTPGmIRiSV5wjQfuEJF9rqF5z28HPvclqjpmRnY3gITsWRsiuNu1zbTOF8YYk1AsyQuua4EGwHwR+U5E3hWRScB8oD7wZz+DqyumZ3enXtFueq1J3Jo8cJds52R2okjslGCMMYnCzugBpapLgF7ANcBMoB4wC7ga6O1NN9VsRnZ3eucvpkFRod+hVKu+eYvYUa8hi1q09TsUY4wxVcTGyQswVd0FPO09TA0rRpjRuhu/mTXR71CqXXjni+7rlvscjTHGmKpgNXnGxLCkeWu2NGjMfqvn+x1Kteu6fgX1C3dZuzxjjEkgVpMXICKSD5ygqj+JyBrK6EGrqlk1E1ndNCO7OwD9cxM/yatXXETv/CXMaNXN71CMMcZUEUvyguUJIC/sfxsmxUc/t+5Ow9076L52md+h1Ij9Vs/j7X5HUyRJMcfuMcYYU3tYkhcgqnpb2P85PoZicDV5ffMWkaLFfodSI/ZbPY9XBp7Mwox29PA7GGOMMZVmbfICSkS+EJFeMab1EJEvajqmuqRIkvilVVf65y7wO5Qas//quQBMa20pnjHGJAJL8oJrGJAeY1o6cGTNhVL3LMhoT0H9hgyoA+3xQjqvX0Xajq1Ma93T71CMMcZUAUvygq1EmzwRqQ8cDeTGuxIR6SMin4vIdhFZJSK3i0jcza5EJElEpoqIisjJ8S5Xm0337nQxoA70rA1JQtl/9Tx+bt3d71CMMcZUAUvyAkRERotIkYgU4RK870LPw8oLgHuAf8W5zubAZ976TsHdEu164LbSlotwCVCnRsmdkd2dJju302X9Sr9DqVH7rZ7HnKzOFOwq8jsUY4wxlWQdL4LlI2At7nai/wAeApZEzLMLmKOqX8W5ziuAVGCEqm4GPhWRdCBHRO73ymLyksS7gJuA5+N9IbXdz6270y93AUl1rIPz/qvmUZSUzMxVmxjUqYXf4RhjjKkES/ICRFV/AH4AEJEtwAequq6Sqx0OfByRzL0B3AcMBd4vY/k7gG+AzysZR62xKymF2VmduWBqWbsm8QzInQfAtOUbLckzxphazi7XBtc04OBoE0TkRBEZEOd6egFzwgtUdRmw3ZsWk7eNC4G/xLmthDCvZQd2pdSvUz1rQ7K2baTtpnymLd/odyjGGGMqyZK84HqEGEkeMNibHo/mwMYo5Ru8aaV5DHhCVcvMdkTkMhGZIiJT1qxZE2dowfRTW5f77r96ns+R+GP/1XMtyTPGmARgSV5wHYi7TBrNJOCAcqwrWsMyiVHuJoqcDfQE7oxrA6rPquogVR2UmZlZjtCCZ0rbPrTaso52m/LKnjkB7bd6His2FLB2606/QzHGGFMJluQFVzLQOMa0xkD9ONezAWgWpbwp0Wv4EJF6wAO4dntJItKMvWP2NRaRtDi3XStNadeHQStnIX4H4pP9V7kazJ+tNs8YY2o1S/KC6wfgshjTLgOmxLmeOUS0vROR9rhEcU7UJdy0dsDDuCRxA/CzN+0N4Kc4t13rrE7LYGXTLAatmOV3KL7pl7eA5CSxJM8YY2o5610bXDnAZyLyPfAybvDj1sD5wH7AcXGuZywwSkTSVHWLV3YWbry9iTGW2QocFVGWDfwbuAVI2FuqTWnbB6BOJ3mNdu+kR6s0frIkzxhjajVL8gJKVb8UkeNxAx8/hmtDVwx8DxxXjnHyngauAf4rIvcBXXAJ5MPhw6qIyAJgoqperKqFwITwlYhIJ+/fGar6fUVfV9BNadeHRrsK6J2/2O9QfDWwYzPe+XElhUXFpCRbhb8xxtRGdvYOMFWdoKqHAmlAeyBdVQ8vR4KHqm4AjsG18Xsfd6eLR4DREbOmePPUaVPa9uaAVXNJ0WK/Q/HVwZ0z2LariFmrSx0r2xhjTIBZTV4toKrbcePaVXT5Wbj73ZY2T6cypi+BxO6LsHVnIbOzOnP1pDF+h+K7gzq7gZAnL17PgHbN/A3GGGNMhViSF2DeJdJzgR5Aw8jpqnpmTceUyH5atoHipGQG1+H2eCGt0hvSKaMR3y1azyVDuvgdjjHGmAqwJC+gRGQgrmPEclySNx037EknYAVQ927HUM2mLNlAUnERB6ya63cogXBw5wzGzcyluFhJSkroSlxjjElI1iYvuB4A3gb64S6TXqyqXYAjcIMY3+9jbAlpytL19FqzhCa7CvwOJRAO6tyCTQW7mZu3peyZjTHGBI4lecG1P/A6rkcteJdrVfVbXOeJe/0JKzEVFhXz07KNdqk2THi7PGOMMbWPJXnBpcAuVVUgH+gYNm050N2XqBLUnNwtbN9VxMCVs/0OJTDat2hE22apfL94nd+hGGOMqQBL8oJrFtDV+38ScJ2IdBeRjsANwELfIktA3y1yiczgFTN9jiRYDurcgsmL1+N+axhjjKlNLMkLrmdxd7gAd5eJ1rjbkC0CDgb+4lNcCemr+WvpmtmY1lus1ircQZ1bsHbrLhau2eZ3KMYYY8rJetcGlKq+Gvb/bBHpDRwKpALfqWq+b8ElmJ2FRXy/eB1nD+7gdyiBc3BYu7xuWU18jsYYY0x5WE1eAIlIQxH5RESGhcpUdauqfqqq71mCV7WmLt3Ajt3FHNGtpd+hBE7nlo1p2aQBk61dnjHG1DqW5AWQqu4ABmO3GasRX81fS0qScEjXDL9DCRwR4eAuLfh24Tprl2eMMbWMJXnB9R5wqt9B1AVfz1/LgR2a06SBtV6IZmj3TPK37GT2ahsvzxhjahP7Vguuj4EHRKQ18BGQhxtWZQ9V/ciPwBLJ+m27+GXVJq47toffoQTW0J6ZAIyfm0+fNuk+R2OMMSZeluQF17+8vyO8RyTFLudW2jcL1qIKR3S39nixtEpvSN826Uycu4Y/HNXN73CMMcbEyZK84OrsdwB1wdfz15LeMIUBbZv6HUqgDeuZydMTF7GpYDdNU+v5HY4xxpg4WJu8APF61PYEUNWlqroUNyDy2tDz8Ie/0dZ+qsrXC9ZyWNeWpCTbR6E0R/XMoqhY+Xr+Wr9DMcYYEyf7ZguWY4E9VUoikgx8CvT0LaIEtmjtNlZuLLBLtXHYv30zmqbWY/xcG73HGGNqC0vygk/8DiBRfTlvDQBDLMkrU0pyEkO6t2TC3DUUF9tQKsYYUxtYkmfqrHG/5NI9qwkdMxr7HUrwiJR4HHX3KNZu3cmsNt2jTt/nYYwxxneW5AVPtGoSqzqpYmu37uSHJesZ3r912TMbAI5c/CMA47sM8jkSY4wx8bAkL3g+FpF8EckHVntln4fKwh/xrlBE+ojI5yKyXURWicjtXnu/0pYZLCIvisgCb7m5IjJaRBpW5sUFxScz8yhWGN4v2+9Qao3M7RsZsHoe47takmeMMbWBDaESLLdV9QpFpDnwGTALOAXXW/chXIJ/aymLnuXNex8wHxgA3OH9Pb2q46xpY39ZTaeMRvTKTvM7lFrlmAWT+fsRvyW3SQbZW+1+tsYYE2SW5AWIqlZ5kgdcAaQCI1R1M/CpiKQDOSJyv1cWzX2quibs+QQR2QE8IyIda/MQLhu372LSwnVcMqQLYu3HyuXXs7/kkSHn8kHvIVzyw//8DscYY0wp7HJt4hsOfByRzL2BS/yGxlooIsEL+cn7m1V14dW8T2flUVisnNjfLtWWV5cNq+iXu4D3eh/pdyjGGGPKYEle4usFzAkvUNVlwHZvWnkcBhQDc6smNH+M/SWXts1S6W93uaiQU2ZNZHrrHixu3sbvUIwxxpTCkrzE1xzYGKV8gzctLiKSDfwVeDXaJV4RuUxEpojIlDVrolUCBsPmHbv5ev5aftUv2y7VVtDJc75EtNhq84wxJuAsyasbog3BIjHKS84oUh94E9gKXBd1A6rPquogVR2UmZlZ4UCr2xez89lVVGy9aiuh9ZZ1DF4+k/f6DLWxfYwxJsAsyUt8G4BmUcqbEr2Gbx/iqrteAfoCJ6rqhqoMrqa9/eMK2jRtyIEd4q7ENFH8ZvaXLMxoz6yszn6HYowxJgZL8hLfHCLa3olIe6AxEW31YngEN/TKKaoaz/yBtXTdNr6av5azBncgKcku1VbGiXO/IaWokPf6DPM7FGOMMTFYkpf4xgIniEj4gHBnAQXAxNIWFJGbgT8C56rq19UXYs349+TlJCcJZw1u73cotV6Lgs0MWfIT7/ceQpHYacQYY4LIzs6J72lgJ/BfETlWRC4DcoCHwztQeHe2eCHs+W+Bu3GXaleKyCFhj+A2uothV2Ex/5m6nKN7ZZHdNCFu2uG7M2Z8xqr0LL6wO2AYY0wgWZKX4Lw2dMcAycD7uLtqPAKMjpg1xZsn5Hjv7wXApIjHSdUXcfX4ZFYua7fu4rcHd/A7lIRxwrxJtNmczz8HneJ3KMYYY6KwO17UAao6Czi6jHk6RTy/AJfgJYTXv19G22apHNm91lVCBlaKFnPejx9y37ALmZ3Zid5rlvgdkjHGmDBWk2cSi0iJx+IWbfl24TrOee8ZkpOTos6z52HK5ZyfP6bh7h28NPDXfodijDEmgiV5JuG9esCJpBQVcub0T/0OJeE027GVEb+M552+R7EuNd3vcIwxxoSxJM8ktPzGzXlt/+H8ZvaXZG2r1UP8BdaFU99jV0p9/r3/r/wOxRhjTBhL8kxCe/KQkRQmp3DNN//2O5SE1X3dcoYs/pFXDziJncnWzNcYY4LCkjyTsFanZfD6/sM5Y8ZndNq42u9wEtoV379NXloGrxxobfOMMSYoLMkzCeuJQ85EBa7+dozfoSS8w5f+zLCFU3jssLPY0DCt7AWMMcZUO0vyTEJakZ7JmP2O58zpn9J+c77f4dQJt0z4J1vrp/Lo4ef4HYoxxhgsyTMJ6uEh5yEKV0+yWrya0mPtMs6a/gn/OuBEFq3Z6nc4xhhT51mSZxLO+C6D+G+/o7l08n9pvWWd3+HUKdd9/RoNCndx37g5fodijDF1niV5JqFsatCYm391NT3WLOWab61HbU3L2raRK75/m49n5vHJzFy/wzHGmDrNkjyTUO48+hLWNG7Ogx89QoOiQr/DqZMum/w2/dqmc8Pb01m1scDvcIwxps6yJM8kjPFz83lrwHFc/v3bDMhd4Hc4dVaDokIeO+dAdhcWc+0b0ygsKvY7JGOMqZMsyTMJYdGarfx5zDS6r11qAx8HQOeWjbnztH5MXrKex76whNsYY/xgSZ6p9fK37OD3L04mSYTn3r6ThkW7/Q7JAKcd0I4RB7blsS/mM+4XG4zaGGNqmiV5plbbtrOQi1+awtotu3jhgsF2Z4ugEAER7jj3UPZfMZurX57MJ90P2VNe5sMYY0ylWZJnaq1N23dzyctTmLV6M0/87gD2b9/M75BMhMa7d/Dym/9Hv7wF/OHUm/i862C/QzLGmDrDkjxTKy1cs5XTnvyGKUvX8+DIARzdq5XfIZkY0nYV8MqY/6NP3mKuPPUWxgw4DvU7KGOMqQMsyTO1zvg5+Zz6xDdsKtjN65cewmkHtPM7JFOG9F3beeXNv3HQil+4cfif+ONvbmBz/UZ+h2WMMQnNkjxTa6zYsJ2rXpvKhS/9QLvmjXj36sMZ3KmF32GZODXduY1Xxvwfoya+zNieh3PShf/g866DrVbPGGOqiSV5dYCI9BGRz0Vku4isEpHbRSQ5juWaisiLIrJBRDaJyGsiklETMYfL3bSDBz+eyzEPTeSLOflcf1wP3rnqMNo1t5qg2iYJ5Q/fvcWbr99IcnExF58xmtPPfYBvOwzwOzRjjEk4omq/oxOZiDQHZgKzgPuArsBDwCOqemsZy44DegJ/AYq95fNUdUhpyw0aNEinTJlSqbh37C5i0qJ1vDF5GZ/NzqeoWDl5QGtuPrE3bZullhZ0pbZras7upGTe6n8sjx12NqvTM+mVv5hTZk3glFkTabN5jd/hGVPjRGSqqg7yOw6TOCzJS3AicjNwA9BRVTd7ZTcAOUB2qCzKcocC3wJDVfVLr+wg4HvgOFX9LNY2K5rkbdq+m7emLuer+Wv5fvE6duwupkXj+owc1I5zBnegU8vGZa/EkrxaZ0dyPd7udwxv9z+GH9v2BqB33iIOWjGTwStm0j93Ae025ZOs5bhzhp3XTC1kSZ6papbkJTgR+RJYpapnh5V1AJYCv1HV92MsdztwmapmR5QvAt5R1etjbbOiSd7arTsZdOdndMlszJHdMzmyR0sO79aSBillXlkOD7Dc2zXBsaxpK97vfSSTOg5gapveFNRvCED9wl10Wb+S9htzabV1PVnbNpCxbSPpO7eRvnMbTXZuJ3X3TlILd9KgcBf1V62gXnIS9ZKFJBFSkoTkJEHs+DABZkmeqWqW5CU4EckHnlTVnIjybUCOqj4QY7k3gSxVHRZR/iGAqp4Ua5uVuVybt3kHrdIbVmhZwJK8BLI7KZlZWV2Ym9mJhRntWJDRnpXpmeQ3acH6Rk0rvN6k4iIESNJiRAEUUUW8LiASdkqUGN1CJJ7zZlpahWM0tdeBHZvz6sUHV2hZS/JMVUvxOwBT7ZoDG6OUb/CmVWS5LpGFInIZcJn3dKuIzC1XlHu1BNZWcNlEYvuhuAhy57ckd37d3g972THhBHo/zAL+dUmFF+9YdZEYY0leXRGt2kFilFdoOVV9Fni2/KFFrFxkiv2Stf0QYvthL9sXju0HY+JnQ6gkvg1AsyjlTYleU1fWcs3KWM4YY4wxAWBJXuKbA/QKLxCR9kBjb1rcy3l6lbGcMcYYYwLAkrzENxY4QUTCW4GfBRQAE8tYLltEjggViMggXHu8sdURqKfSl3wThO0Hx/bDXrYvHNsPxsTJetcmOG8w5FnAL7jBjLsADwN/Dx8MWUQWABNV9eKwsnFAD/YdDDm/rMGQjTHGGOM/q8lLcKq6ATgGSAbeB24DHgFGR8ya4s0T7mxcbd8/gVeAqcBp1RmvMcYYY6qG1eQZY4wxxiQgq8kzvhORPiLyuYhsF5FVInK7iJTjNheJQUS6icgzIvKziBSJyAS/Y/KDiIwUkfdEZKWIbBWRqSJyjt9x1TQROUNEvhWRdSKyQ0TmisitIlLf79j8JCJtveNCRaSJ3/EYE2Q2Tp7xlddm8DNcu8FTgK7AQ7gfILeWsmgi6gucCHwH1OUv8j8Di4HrcIPengi8LiItVfUxXyOrWRnAeOAB3LBFB+Hdcxq42reo/PcAsBU3QoAxphR2udb4SkRuBm4AOqrqZq/sBrwvs1BZXSAiSapa7P3/H6Bl5G3l6gIvmVsbUfY6cKiqdvYprEAQkbuAPwDNtQ6evEVkCPAucDcu2UtT1a3+RmVMcNnlWuO34cDHEcncG0AqMNSfkPwRSvDqusgEz/MTkFXTsQTQOupoLa/XhOMx4HYCfFszY4LEkjzjtxKDK6vqMmA70QdjNnXTYbhL+nWOiCSLSCNvzMprgKfqYi0ecAXQEHjC70CMqS2sTZ7xW3Oi3yZtgzfN1HEicgyuveZFfsfik21AA+//V4BRPsbiCxHJAO4AzlXV3SLid0jG1ApWk2eCIFqthMQoN3WIiHQCXgfeVdWX/I3GN4cBQ4Drccnu4/6G44u7gO9V9SO/AzGmNrGaPOO3DUCzKOVNiV7DZ+oIEWmBu4XeMuBcn8Pxjar+6P37tYisBV4WkYdUdaGfcdUUEemLq8U9UkSaecWNvL9NRaRIVQt8Cc6YgLMkz/htDhFt70SkPW54hDlRlzAJT0QaAR/gOhmcpKrbfA4pKEIJX2egTiR5QHegHjApyrQVwAvAJTUakTG1hCV5xm9jgVEikqaqW7yys4AC3C3VTB0jIinAW7gv98NVNd/nkILkcO/vYl+jqFlfA0dFlP0KuBE3huKiGo/ImFrCkjzjt6dxPQb/KyL3AV1wY+Q9XJfGyIM9tVcnek/bAukicob3/CNV3e5PZDXuSdx++BPQQkQOCZv2k6ru9CesmiUi43ADhc8EinAJ3vXAmLpyqRb2DKkzIbzMa6sJ8JWNk2dMbDYYsvGdiPTBNSY/FNcO73kgR1WL/IyrpnlfXLFqaDqr6pKai8Y/IrIE6Bhjcl3aD3cApwGdgEJcjdWLwNOqutvH0HwnIhfg9oUNhmxMKSzJM8YYY4xJQDaEijHGGGNMArIkzxhjjDEmAVmSZ4wxxhiTgCzJM8YYY4xJQJbkGWOMMcYkIEvyjDHGGGMSkCV5xhhjjDEJyJI8Y4wxxpgEZEmeMcbEICL1/Y7BGGMqypI8Y0y1EJGhIqIiMjysrLOI5IvIP+Jcx+9E5EsRWSsiW0VkkogcGjHPbBF5LMqy/xSRKWHPU0RklIgsEJECEZkiIkeETU8SkW0icq2IPCoia4Bp5YijhYi8ICIbvPluFpG/isiciPlKjcMYY6qK3dbMGFNtROQLoKGqHiYiTYFvcffnPSWeexOLyN3AQm+ZBsClwOFAe1Xd5c3zH6CZqh4btlx3YDZwsqqOE5EUYBzQB7gNdx/YS4DhQHdVzRORbsB8YDXwP+AdYJeqTiwrDhFp4L22JsAduHsw3wWkA5NV9SwvrjLjKMfuNcaYUqX4HYAxJqGNBr4UkeOB64HdwNnxJHgAqnpL6H8vQVoEzAG64pI4gFnARRGL5gCTVHWc9/x64GBgoKrO89Y3AVgGnAE8AQzw5v2nqt5azjhuAroD3VQ135tvE/Al8FzYquKJwxhjqoQlecaYaqOqX4nIZ7hasY3Awaq6NZ5lRSQV+CNwHtAFaBQ2eXvY/zOBtiKSpqpbRKQvcDZwlLeeJFxy9QqwyEvSABRYAHTwnvf31ntXeeLw1n818EgowfMs9v7+XM44jDGmSlibPGNMdVuAS4xGq+qKeBYQEQE+Aq4BXgROBQYDT+ESseVhs8/0/vb0/t4OfKaqX3rP+wOZwFW4msTwxxHA5rD5JqhqQTnjGAC0BN6PeBltvb/TyxmHMcZUCavJM8ZUGxG5DHcp9Wdc27Pn41z0SGAYcIiqfh+2vgeAGapaHDbvPKAQ6C0iRcBpuEuiIa29v8cCm6Jsa6n3dwAwprxxiEho/flRlt2gqqGENN44jDGmSliSZ4ypFiJyHPA4LrmbB0wSkeGqOjaOxdt5f+eFre9XuITr2fAZvY4PC4BewFnAu6r6Q9gsq72/G1V1aoxYU3Ht636uQBxrvb/dcG3r8DqZXBuxvjLjMMaYqmRJnjGmynnt4t4C7lfVV7yyz3A9SseGzTcMGA8cpaoTwlbxI1AMPCoiL+Mukf4e134tMhEDd8n2TFybuf2jTJsGvC4idwFLcJdNDwJmqerLQF9c85XIdccTx8+4y7b/EJGbcefVW4DG3nbLE4cxxlQZa5NnjKlSIpIFfAB8CvwtbNIdwGAROSmsLNSJYZ9Lnao6G/gDcBzwX+AA3LAlQuwkrxswRlVnRKyrEPg1MAW4F/gYeADXZm6SN1uo08XC8sbhDeUyEte27k3gr8CdQBHwVTnjMMaYKmPj5BljfCMitwFHqupRfsdSlUTkGuBWoIOq7vA7HmNM3WSXa40xfjoMeNjvICrDu+R8GK6Grh5wIq6271xL8IwxfrKaPGOMqQQRORF4EOiMa783BbhLVT/xNTBjTJ1nSZ4xxhhjTAKyjhfGGGOMMQnIkjxjjDHGmARkSZ4xxhhjTAKyJM8YY4wxJgFZkmeMMcYYk4AsyTPGGGOMSUCW5BljjDHGJKD/ByLbc62npyLxAAAAAElFTkSuQmCC\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N=[5, 10, 50, 100]\n", "weibull_mean = {}\n", "colors = iter(['y', 'r', 'g', 'pink']) # iterable colors\n", "shape = 1\n", "import math\n", "for k in range(len(N)):\n", " temp_mean = []\n", " for i in range(1000): \n", " weibull = np.random.weibull(shape, N[k]) \n", " temp_mean.append(np.mean(weibull))\n", " weibull_mean[N[k]] = np.asarray(temp_mean)\n", " # let's build histogram for Weibull sample averages \n", " plt.hist(weibull_mean[N[k]], color=next(colors), density=True, label=f'N = {N[k]}')\n", " plt.legend()\n", " plt.ylabel('Fraction of samples')\n", " plt.xlabel('$x, average$')\n", " plt.title(f'Weibull sample averages histogram, shape k={shape}, sample size N = {N[k]}')\n", " \n", " # let's build a corresponding Normal distribution PDF for the current N\n", " norm_rv = sts.norm(loc = 1, scale = math.sqrt(1/N[k]))\n", " pdf = norm_rv.pdf(x)\n", " plt.plot(x, pdf, label=f'PDF of N(1, {1/N[k]})' )\n", " plt.legend() \n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Some theory \n", "## Count the Normal distribution parameters: mean and variance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[The Central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem), allows us to approximate the distribution of sample averages is a **Normal distribution**. Using information about the *mean* and *variance* of the original [Weibull] distribution we calculate the parameters of that resulting Normal distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have for the taken Weibull ditribution: ${\\bf λ = 1 ; k = 1}$\n", "\n", "Then the Weibull ditribution parameters are the following: \n", "$${\\bf mean_w = 1}$$\n", "$${\\bf \\sigma_w^2 } = \\lambda^2 * \\left( \\left(1+\\frac{2}{k}\\right) - \\left(1+\\frac{1}{k}\\right) \\right)^2 = \\left( \\left(1+2\\right) - \\left(1+1\\right) \\right)^2 = (3-2)^2 = 1^2 = 1$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the *Central limit theorem*, the Normal distribution $N(mean_N, \\sigma_N^2)$, of sample averages should have the following parameters:\n", "\n", "$$ mean_N = mean_w = 1$$\n", "$$\\sigma_N^2 = \\frac{\\sigma_w^2}{n} = \\frac{1}{n}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison of sample averages approximations\n", "\n", "Let's show the difference between the obtained distributions for different values of **N** (volume of samples). Below is the function of the accuracy of the approximation of the distribution of sample avarages to Normal distribution change with increasing **N**: \n", "\n", "| N, samples | $ {\\bf \\sigma^2}$ | ${\\bf \\sigma}$ |\n", "| --- | --- | --- |\n", "| 5 | 0.2 | 0.45 |\n", "| 10 | 0.1 | 0.32 |\n", "| 50 | 0.02 | 0.14 |\n", "| 100 | 0.01 | 0.1 |\n", "\n", "### Conclusion\n", "The distribution of sample avarages (of a smooth distribution) might be quite exactly approximated with a Normal distribution with parameters: \n", "$$ mean_N = mean_{original}$$ \n", "$$\\sigma_N = \\frac{\\sigma_{original}^2}{\\sqrt{n}}$$\n", "As **N** grows, the accuracy of the approximation of sample avarages grows, since a standard deviation ${\\bf \\sigma}$ decreases by a factor of ${\\bf \\sqrt{N}}$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }