{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Skewed distribution\n", "\n", "##### Germain Salvato Vallverdu [germain.vallverdu@univ-pau.fr](germain.vallverdu@univ-pau.fr)\n", "\n", "This cookbook shows how to plot a skewed distribution from the normal probability density function and its cummulative density function. You can take a look at [this wikipedia page](https://en.wikipedia.org/wiki/Skewness) giving an introduction to skewness of a distribution.\n", "\n", "This cookbook was written from [this question](http://stackoverflow.com/questions/15400850/scipy-optimize-curve-fit-unable-to-fit-shifted-skewed-gaussian-curve) on stackexchange.\n", "\n", "### import modules and setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab --no-import-all inline\n", "\n", "from scipy.special import erf\n", "from scipy.optimize import curve_fit\n", "\n", "matplotlib.rcParams[\"figure.figsize\"] = (10, 6)\n", "matplotlib.rcParams['lines.linewidth'] = 2\n", "matplotlib.rcParams[\"font.family\"] = \"sans\"\n", "matplotlib.rcParams[\"font.size\"] = 20" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Definition of functions\n", "\n", "The normal probability function reads \n", "\n", "\\begin{equation}\n", " \\text{pdf}(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}} \\exp\\left(- \\frac{(x - \\mu)^2}{2\\sigma^2} \\right)\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def normpdf(x, mu, sigma):\n", " return 1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sigma**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cummulative density function reads \n", "\n", "\\begin{equation}\n", " \\text{cdf}(x) = \\frac{1}{2} \\left[1 + \\text{erf}\\left(\\frac{x - \\mu}{\\sigma\\sqrt{2}} \\right) \\right]\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def normcdf(x, mu, sigma, alpha=1):\n", " return 0.5 * (1 + erf(alpha * (x - mu) / (sigma * np.sqrt(2))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to add skewness to the normal probability density function, it is multiplied by the normal cummulative density function. In order to adjust the skewness of the distribution, a parameter $\\alpha$ is added to the cummulative density function and we get a skewed density function which reads \n", "\n", "\\begin{equation}\n", " \\text{skewed}(x) = \\frac{A}{2\\sigma \\sqrt{2\\pi}} \\, \\exp\\left(- \\frac{(x - \\mu)^2}{2\\sigma^2} \\right)\n", " \\left[1 + \\text{erf}\\left(\\alpha \\, \\frac{x - \\mu}{\\sigma\\sqrt{2}} \\right) \\right]\n", "\\end{equation}\n", "\n", "The prefactor $A$ is added for fitting purpose." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def skewed(x, mu, sigma, alpha, a):\n", " return a * normpdf(x, mu, sigma) * normcdf(x, mu, sigma, alpha)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot examples\n", "\n", "The plots below show the effect of parameter $\\alpha$ in the $\\text{cdf}$ part of the skewed distribution. With $\\alpha$=0 we get the normal distribution." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ax1.set_ylabel?" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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uv3XrVmbNmtXjODNnzmTbtm2JTLqKAeMztO1vA2DExBHd1hV8rgCAmgdrtAOo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\nbnFx0K2bg67xC4jfn8LE324G8h8mAdJjN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lwi8HvrgAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(14, 6))\n", "x = np.linspace(-5, 5, 200)\n", "for alpha in [0, 1, 2, 5, 10]:\n", " ax1.plot(x, skewed(x, mu=1, sigma=1, alpha=alpha, a=1), label=r\"$\\alpha$=%d\" % alpha)\n", "ax1.set_title(\"Positive skewness\")\n", "ax1.legend(loc=\"upper left\", fontsize=16)\n", "for alpha in [0, 1, 2, 5, 10]:\n", " ax2.plot(x, skewed(x, mu=1, sigma=1, alpha=-alpha, a=1), label=r\"$\\alpha$=%d\" % -alpha)\n", "ax2.legend(loc=\"upper left\", fontsize=16)\n", "ax2.set_title(\"Negative skewness\")\n", "ax2.set_yticklabels([])\n", "ax2.set_xlim(-4, 6)\n", "fig.subplots_adjust(wspace=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit to a skewed distribution\n", "\n", "In order to fit some datas to the skewed distribution, we will use the `curve_fit` method of `scipy.optimize`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function curve_fit in module scipy.optimize.minpack:\n", "\n", "curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, check_finite=True, **kw)\n", " Use non-linear least squares to fit a function, f, to data.\n", " \n", " Assumes ``ydata = f(xdata, *params) + eps``\n", " \n", " Parameters\n", " ----------\n", " f : callable\n", " The model function, f(x, ...). It must take the independent\n", " variable as the first argument and the parameters to fit as\n", " separate remaining arguments.\n", " xdata : An M-length sequence or an (k,M)-shaped array\n", " for functions with k predictors.\n", " The independent variable where the data is measured.\n", " ydata : M-length sequence\n", " The dependent data --- nominally f(xdata, ...)\n", " p0 : None, scalar, or N-length sequence, optional\n", " Initial guess for the parameters. If None, then the initial\n", " values will all be 1 (if the number of parameters for the function\n", " can be determined using introspection, otherwise a ValueError\n", " is raised).\n", " sigma : None or M-length sequence, optional\n", " If not None, the uncertainties in the ydata array. These are used as\n", " weights in the least-squares problem\n", " i.e. minimising ``np.sum( ((f(xdata, *popt) - ydata) / sigma)**2 )``\n", " If None, the uncertainties are assumed to be 1.\n", " absolute_sigma : bool, optional\n", " If False, `sigma` denotes relative weights of the data points.\n", " The returned covariance matrix `pcov` is based on *estimated*\n", " errors in the data, and is not affected by the overall\n", " magnitude of the values in `sigma`. Only the relative\n", " magnitudes of the `sigma` values matter.\n", " \n", " If True, `sigma` describes one standard deviation errors of\n", " the input data points. The estimated covariance in `pcov` is\n", " based on these values.\n", " check_finite : bool, optional\n", " If True, check that the input arrays do not contain nans of infs,\n", " and raise a ValueError if they do. Setting this parameter to\n", " False may silently produce nonsensical results if the input arrays\n", " do contain nans.\n", " Default is True.\n", " \n", " Returns\n", " -------\n", " popt : array\n", " Optimal values for the parameters so that the sum of the squared error\n", " of ``f(xdata, *popt) - ydata`` is minimized\n", " pcov : 2d array\n", " The estimated covariance of popt. The diagonals provide the variance\n", " of the parameter estimate. To compute one standard deviation errors\n", " on the parameters use ``perr = np.sqrt(np.diag(pcov))``.\n", " \n", " How the `sigma` parameter affects the estimated covariance\n", " depends on `absolute_sigma` argument, as described above.\n", " \n", " Raises\n", " ------\n", " OptimizeWarning\n", " if covariance of the parameters can not be estimated.\n", " \n", " ValueError\n", " if ydata and xdata contain NaNs.\n", " \n", " See Also\n", " --------\n", " leastsq\n", " \n", " Notes\n", " -----\n", " The algorithm uses the Levenberg-Marquardt algorithm through `leastsq`.\n", " Additional keyword arguments are passed directly to that algorithm.\n", " \n", " Examples\n", " --------\n", " >>> import numpy as np\n", " >>> from scipy.optimize import curve_fit\n", " >>> def func(x, a, b, c):\n", " ... return a * np.exp(-b * x) + c\n", " \n", " >>> xdata = np.linspace(0, 4, 50)\n", " >>> y = func(xdata, 2.5, 1.3, 0.5)\n", " >>> ydata = y + 0.2 * np.random.normal(size=len(xdata))\n", " \n", " >>> popt, pcov = curve_fit(func, xdata, ydata)\n", "\n" ] } ], "source": [ "help(curve_fit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, compute points representing a skewed distribution with a random noise." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# produce data to fit\n", "sigma = 10\n", "mu = 50\n", "alpha = 2\n", "a = 1\n", "x = np.linspace(0,100,100)\n", "\n", "y = skewed(x, mu, sigma, alpha=alpha, a=a)\n", "yn = y + 0.002 * np.random.normal(size=len(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we use `curve_fit` to optimize the parameters and then plot the resulting functions." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parameters skewed :\n", "-------------------\n", "mu : 50.0876601397\n", "sigma : 9.76673500085\n", "alpha : 1.94006355233\n", "a : 0.976838902518\n", "\n", "Parameters normal :\n", "-------------------\n", "mu : 56.9087655557\n", "sigma : 14.5346539279\n" ] }, { "data": { "image/png": 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La99e688/z1eOvH/eTd4/74QbR68roz7hLEopbbFYSExMLOoY5HUXJSW/LyVntVqxWCye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\nM1HhxiX2FXtWeDiqEnjhBahSBb7+Gn7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yi9XReE0mEQXO2T3OpmVsS1bvXE3+oXyrw/Gd\nFi2qa9I+9JBZ/lWIICVJpxAiNJWVVf/YTppk6haGGGnpDJz4mHgG9RwEwMLNYTb+8YYbzOpbziVg\nhQhSknQKIULTq6/C5s3Qty9cd53V0XitsLSQTfs2ERcdxzHtj7E6nIgQlqWTwCyL+eij5vIjj0Bx\nsbXxCOGGJJ1CiNBz+DBMnmwuP/GE+dENMat3rgYgrUMacdGhNRY1VDnHdX6x+YvwKZ3kNGIE9OsH\n+fnw0ktWRyOES5J0CiFCz7PPwq5dcOaZcOmlVkfTJNK1Hng92/TkuA7Hcaj0EMu3Lbc6HN+KioIp\nU8zlJ56AgwetjUcIFyTpFEKEll274JlnzOWnnoIQLTUkSac1MvpmADAne47FkfjBkCFwzjmwd2/1\nd0SIICJJpxAitDz+uOleHzYMzj3X6miaTGauW2N43+EAzM2eiw63VXyUMgdiYHoDduywNh4h6pCk\nUwgROrZsgZdfNj+uTzxhdTRNVmGvYM3ONQCc1Okki6OJLMe3OZ72Ce3ZdnBb1bjasNK/P1x2mZlM\nNGmS1dEIUYsknUKI0OGsQ3jddXDCCVZH02TZe7IprSyl55E9aZ3Q2upwIkJFRQVjx87khOOXs+e7\ngQD8a9oUKioqLI7MD554AqKj4fXXYf16q6MRoooknUKI0LByJbz/vll1yDlzPUTJeM7AGz9+FllZ\nw8jJGQq/jwRgxb5NjB8/y9rA/KFvX7jpJrMspnOZTCGCgCSdQojQ4PzxvP12SEmxNpZmkqQzsGw2\nG7NntwQSzRVbzoeyROj6C58sKsZms1kan19MnAiJiTBnDnz7rdXRCAFI0imECAVffQULF8IRR8D9\n91sdTbPJJKLAKigoIC+vxoFKRQvYPBiA/JabKCgosCgyP0pOhrvuMpfvvhvCbdKUCEmSdAohgpvd\nbn40Ae65B9q1szaeZtJaS0tngCUnJ9OjR27tK7PNLPaEkxaQnJxsQVQBcPfd0KED/O9/MHu21dEI\nIUmnECLIvf8+/PILdO0Kd95pdTTNVnC4gD22PbRJaEP3I7pbHU5ESExMJCPjMFCjG33jMNCKsq6r\nqIyutCw2v0pKgocfNpcnTIBwnDQlQooknUKI4FVcXN2d/vjjZoxaiKvZyqlCtLB9KMrMvIwxY+aT\nmrqA6Oh1pHb4ieTKPlSqChZuXmh1eP5zyy3QuzdkZ8Mbb1gdjYhwknQKIYLXtGmQl2fWlP7b36yO\nxieka90aMTExTJs2gnXr0snOTmDdunTGDvkHYArFh624uOrlMSdONAsrCGERSTqFEMFp167qAvCZ\nmabuYBiQpNNaiYmJ9O7d23S5O5bEnL9xPhX2MO56HjECzjgD/vijesUiISwgSacQIjhNmgSFhWa5\ny/PPtzoan1n5x0pAViIKBn3b96VPuz7sK97Ht7lhXFZIKbMsJpgDuLw8a+MREUuSTiFE8Fm/Hl55\nxbRuPv201dH4zIGSA2zat4mEmASO63Cc1eEIqGrtDOsudoABA+Cqq6CkJCzKjonQJEmnECL43HMP\nVFbCzTfDceGTnP204yfAdK3HRsdaHI0AGN7XlE6akz0HHe61LJ980ozxfPdd+PFHq6MREUiSTiFE\ncPnqK/j0U2jVynSxh5Ef8n8A4LQup1kciXDq360/7RPbs3n/ZtbvCfN1ynv2hLFjzeVx46RgvAg4\nSTqFEMHDbofx483l++6DTp2sjcfHftxhWpck6Qwe0VHRXNznYgBm/x4BBdTvv98UjP/mG/jkE6uj\nERFGkk4hRPCYPh1WroRu3cKiEHxdP+abpLNzZefwXO87RF12zGUAfPzbxxZHEgCtW8PkyebyPfdA\naam18YiIIkmnECI4HDpkWjfBlEoKg0LwNeXuzyW/MB9VlsiFp3UmLW0ZY8fOpEJWibHc4N6DOSL+\nCFb+sZKNezdaHY7/3XSTGSu9dSs8/7zV0YgIIkmnECI4PP447NwJ/fvDtddaHY3P3TblBQD09jPR\n9hPIyRlKVtYwxo+fZXFkIiEmoWoW+0frPrI4mgCIiYGpU83lRx+F3butjUdEDEk6hRDW27gRnnvO\nXM7KMnUFw4jNZuPrzbnmPztqjudMZM6cltLVHgQuPepSAD5Y+4HFkQTIkCFw4YWmh8G5PrsQfhbQ\npFMp1VUp9YZSKl8pVaKU2qqUek4pdaS/tqOUilFKjXHcf6VSqlQpZVdK/cOD57leKfW9UqpQKXVA\nKbVEKTXMm1iFEB646y4oL4cbboDTwm+STUFBAYdaOQpy59d+fXl5KRQUFFgQlQCoqKhg7NiZjLs0\nBkqSWLt7LX8fNy0yhj1MnWpq4b7yCvz6q9XRiAgQsKRTKdUL+AW4HlgBPAtsBsYA3yml2vhpOy2B\n5xz37wQUAI3WiVBKZQJvAp2BV4B3gOOBeUqpUZ7EKoTwwMKFMG+eKZHkXCM6zHTu3JmormvMf3bU\nTjq7d99GcnKyBVEJgPHjZ5GVNYxtW4bD+isAeOeXvZEx7CEtDW6/3VSNGD1aSigJvwtkS+fLQHtg\ntNb6Cq31/VrrP2MSwmOAx/20HRswFOiite6CSSQbpJTqD4wDNgInaK3v0lqPBk4B9gGZSqkeHsYr\nhHCnvLx6lvpDD0HnztbG4yd/lP6BPaEQDneEg91r3GIjI6OIxDCbNBUqbDYbs2e3BBzv/7qrzXna\nrMgZ9jBpUnUJpRkzrI5GhLmAJJ2O1skLgByt9Ut1bp4IFAHXKaVa+Ho7WutyrfVCrfVOL0K+FdMa\n+rjW+lCNbeUCLwLxwA1ebE8I4cpLL5klL486CsaMsToav3EWhe8Z143U1M+Ijl5HauoCxoyZT2bm\nZRZHF7kKCgrIy0upvmLL+VDcBjquI7ekPDKGPRx5pFmpCODuu+HwYWvjEWEtUC2d5znOv6h7g9b6\nMPAt5lDzzABtpzHO51no4rbPAAUMauZzCBHZdu+GiRPN5Wefhfh4a+PxI2dR+JGDM1i3Lp3s7ATW\nrUtn2rQRxMTEWBxd5EpOTqZHj9zqK+yxsP5yAJLO/DByhj2MHGnGUu/YYapICOEngUo6+2JaDje4\nud1ZGK1PgLbjllIqEegKHHbTOtrs5xBCYLrTDx6EwYPh4outjsavaq5ElJiYSO/evaVLPQgkJiaS\nkXEYMwrLYa3pYo864WtatGiw8y18REVV1+ucOtVUkxDCDwKVdLZ2nB90c7vz+sZmsftqO359jqVL\nl6KUcnsSIuL99JOZMRsTY0olhfH3osJewS8FvwBwWtfwm5kf6jIzL2PMmPmkpi4gOnodKbqEBHsS\n+6PzWbtrrdXhBc4ZZ5jqEeXl1euzi7ARLDmJ9OtYYOnSpVaHIBqQk5Mjn5E/2e3w+uswcCAMGAC7\ndpmTDwTjZ7fz8E5OLz+dI+OPZO0PEZTENIFVn9+ll3Zg2LByCguzSUpKYuGWW/j5j5+ZuWAme3vu\nDXg8lrn8ctPFbrOZg8I+3nXoBeP3TwSXQCWdztbB1m5ud15/IEDb8etzpKens2TJkmaEIKy0dOlS\n0tPTrQ4jfL38Mrz/PnTtWl0qyUeC8bN7/ZfXWfrzUq466qqgiy3YBMvnF701mqnTp5J/OJ9HBj5S\nrzXIZrNRUFBAcnJy+A2T2LgRxo2D7dth7VqvxloHy+cn6tMNlMMKZGtnoLrXszGTb9wdNh3tOHc3\nVtPX23FLa20D8oFWSqlO/ngOISLWzp0wYYK5nJXl04QzWNUczylCw7kp59KxZUc27tvIqp2rqq53\nFpJPS1tGnz4lpKUtY+zYmeFVSP7228267Js2wVNPWR2NCDOBSjqdzX6D696glGoFnIUZyb0iQNtp\nzFeO8yEubrvIcb64mc8hROS55x4zeWjIENOVFwEk6Qw9MVExXHGsKRT/4doPq653FpLPyRmK3Z5G\nTs5QsrKGhVch+dhYU8oMzGINMqlI+FBAkk6t9RZMmaNUpdTtdW6ejFk1aLrWuhiqlq7s66jL2eTt\nNMO/MS2qD9RcWlMplQrcBpQAbzXzOYSILF9/DdOnm+66558P68lDTiUVJazeuRqF4k/Jf7I6HOGF\nq9PMLPaPfvsIrXX9QvJVEsOvkPzAgXD99VBaCqNGyUpFwmcCOZFoFKaOZpZS6nxgPaaeZjrwO/Bg\njft2ddyeA9RKPL3cDgBKqXsxqxUB9MMklP9QSp3juO4brfXrzvtrrf+nlHoWuBNYrZT6GIgDrsbM\nWr/dUSheCOGJ8nLz4wWme/2oo6yNJ0BW/bGKCnsFx3U4jqT4JKvDEV44u8fZdG7VmS37t/BD/g+0\nL21fu5B8DXl5KRQUFNC7d+8AR+lHmZlmzPWXX5qViq65xuqIRBgI2DKYjlbKUzEthKdjlpnsiVm+\nsr/Wen/dh+BijfQmbAdMN/nfHacTHdvtX+O6s1w8z3jMqkMFwM3AdcAa4GKt9csev3AhhBm/uW4d\n9O4N995rdTQB41yJ6PSup1scifBWdFQ01xxvEq23V71dv5B8Dd27bwu/QvLt28Mzz5jLd94J+139\ntArhnUCuvY7WOl9rfaPWuqvWOkFr3dOxrvnBOvfbprWO1lq7PGz0dDs17n+eY3vuTv9w87jpWusz\ntNZJWuvWWutBWuvPmv9OCBFB8vLM+s4AL7wACQmWhhNIMp4ztI3sNxKAGWtnEBUXVb+QPAA2MjKK\nwm8WO5iVis4+25Q0u/9+q6MRYSCgSacQIsJobWbDFhXBFVeYCUQRRJLO0NY7qTfHtz2eAyUHmP37\n7HqF5FNTFzBmzHwyMy+zOlT/iIqCf//bLOLwn//AiubO0RWRTpJOIYT/zJwJc+fCEUfAtGlWRxNQ\nh0oPkb0nm9ioWE7sdKLV4Qgv1CyNtO7dDADu++BJAKZNG8G6delkZyewbl0606aNICYmjNdZSUuD\n8ePNAeQ//wnhVB5KBJwknUII/9i7F0aPNpeffhq6dbM2ngD7ecfPaDQndT6J+BjPC2wL69UsjaTX\njIOKOLbFrOafd78GmDXbe/fuHZ5d6q489BD07AmrV5vx2UI0kSSdQgj/uOsuMxbs3HPh5putjibg\nnJOIpGs9tNQrjVTcFrIzQGn+u/l/4VUayVOJifDii+byQw/B5s3WxiNCliSdQgjfW7QI3n7b1OR8\n9VUzNizCfJP3DQBndjvT4kiENwoKCuqXRlp5AwAHUpeyY8cOC6IKAkOHmrJJxcXmINJutzoiEYIi\n75dACOFfRUVwyy3m8sSJ0MfdqrXhq9JeyfJtywEYmDLQ4miEN1yWRtpyARQmQ7tcttm3WRNYMMjK\ngg4dYMkSeOUVq6MRIUiSTiGEbz30EOTkQL9+ZgJCBFqzaw0HSw+S0jqFlCNdFxQXwSkxMbF+aSR7\nDKz6KwAzfp9hTWDBoH376m72u++GXFkjRXhHkk4hhO/88INpDYmKgtdeM+s4R6Cvt30NwMBUaeUM\nRa5KI/39hB4AfLjuQ4rKiiyO0EJXXgmXXw6HD5seDVkiU3hBkk4hhG+UlcFNN5mxXnfdBaecYnVE\nllm2bRkA5/Y41+JIRFPExMTUK4309rNj6N+tP4fLDvPf9f+1OkTrKGVaO9u0gYULzdhtITwkSacQ\nwjceeQTWrDFLXTpXIIpAWmtp6QwTdUsjOVcoevPXNy2MKgh07lxdOunOOyFSJ1cJr0nSKYRovhUr\n4MknTSvIW2+ZEisRav2e9eyx7SG5VTK927hcyVeEqKvTrqZFTAuW5Cxh6/6tVodjrb/9DS66CA4c\ngFtvlW524RFJOoUQzVNUBH//u+lWv/tus1ZzBKvZyqmUsjga4UutE1pz+bGXAzB91XSLo7GYUmZp\nzCOOMKuOvf++1RGJECBJpxCiee69FzZuhOOPh8mTrY7GcjKeM7w5u9jf+PUNKuwRviRkt24wdaq5\nfNttcPCgtfGIoCdJpxCi6RYtMpMKYmPhnXdMMfgIJuM5w9+gnoM4uu3R5B7MZW72XKvDsd6NN8Il\nl5iEc/ZsKRovGiRJpxCiafbvhxvMSi1MnGjqcka4zfs3s6NwB+0T23Ns+2OtDkf4QZSK4vbTbwfg\n+R+etziaIKCUKY/WsaOpz/vss1ZHJIKYJJ1CiKa54w7Iz4czzjBd7KKqlfPclHNlPGcYG9lvJK3i\nWrE0Zymrd662OhzrdewIr79uLj/wAKyW90S4JkmnEMJ7n3wC774LLVrA9OkQE2N1REFBxnNGhiPi\nj+CGfqaV//nvpbUTgIsvNrV5y8rg2muhpMTqiEQQkqRTCOGdvLzqtdWffjoi11Z3R8ZzRg5nF/u7\na95lr22vxdEEicGD4eijYe1auP9+q6MRQUiSTiGE5yoqTCvGvn0wdCiMGmV1REEj92AuOQdyaB3f\nmhM6nmB1OMLP+rTrw5CjhlBSUcJrv7xmdTjBIS7O9IBER8Nzz8HixVZHJIKMJJ1CCM9NngzLl0Ny\nsikCHyW7ECdnK+c5KecQHRVtcTQiEO44/Q4AXvzxRSmf5HT66WZiIcD118NeaQUW1eQXQwjhmSVL\n4LHHzGzVd981kwdElWU5Mp4z0lx41IUc3fZo8g7lMef3OVaHEzwmTIABA8xEQ+fCEUIgSacQwhO7\nd5tuda3hwQdh0CCrIwo6X+fKeM5II+WT3IiJgRkzoG1bWLAAnnnG6ohEkJCkUwjRMLvddJMVFJgl\nLh9+2OqIgk5BYQEb9m6gZWxLTu58stXhiABylk9atm0Zn/70KTabzeqQgkOPHqayBZgySt98Y208\nIihI0imEaNi0afDZZ9CmjVlfWcoj1bM8dzkAZ/U4i9joWIujEYGUGJ1I70NnA3DJo2+SlraMsWNn\nUlEhYzwZNgzuuQcqK+Hqq02PiYhoknQKIdz74Qe47z5z+a23oHt3S8MJVjKeM3KNHz+LVa8+af5z\nwgJydp1GVtYwxo+fZW1gweKxx+Css2DHDrjuOhnfGeEk6RRCuLZrF1xxBZSXm9WHhg+3OqKgJeM5\nI5PNZmP27Jaw9yTYOARiS+DUl4FE5sxpKV3tALGx8MEH0K4dLFwITz5pdUTCQpJ0CiHqKy+Hq66C\n7dvNLFSZCODWHtse1u5aS0JMAqd1Oc3qcEQAFRQUkJeXYv7z3XhzfuY0iCskLy+FgoIC64ILJt26\nwTvvmMsPPQTLllkbj7CMJJ1CiPruvtv8MCQnw8cfm6LPwqWFmxYCcFb3s4iPibc4GhFIycnJ9OiR\na/6zdRDkngWJ++D0F+jefRvJycnWBhhMhg41pZTsdnNAm5dndUT12Gw2Nm/eLC3UfiRJpxCitnff\nhaws0y328ccm8RRuzd0wF4AB7QbIj1WESUxMJCPjMGADFCxzVHYYMJWhGXtJTEy0MrzgM3kynH++\nGbpz6aUQJN+XiooKxo6dSVraMvr0KZHJYH4kSacQotrKldXrqmdlma514Zat1MbstfMAeOzvZ8mP\nVQTKzLyMMWPmk5q6gKicLsTvOgYS99LjinyrQws+MTHw4YfQqxf88gvceKOp/Wux8eNnkZU1jJyc\nodjtaeTkDJXJYH4iSacQwti7Fy6/HIqL4YYb4F//sjqioPe3B56gTBXDzuPR+y6UH6sIFBMTw7Rp\nI1i3Lp0N2S34YNQTADy74lmKyoosji4ItWsHc+dCq1ZmgtHTT1saTtVkMOq2SstkMH+QpFMIARUV\n8Ne/Qk4OnHoqvPSSWe5SuGWz2fgyb5X5z4ZLatxifqz27Nkj48MiSGJiIr179ybjuAxO63Iau227\n+fdP/7Y6rOCUlmaG8YAZ5zl/vmWh1JoMVodMBvO9gCadSqmuSqk3lFL5SqkSpdRWpdRzSqkj/b0d\npdQApdQCpdRepZRNKbVKKTVGKVXvPVBKXa+UsjdwuqUpr1+IoKQ13H47LFoEHTrAf/8LCQlWRxX0\nduzYQWGXn81/smuWk6ogJ2cb/fp9J+PDIpBSiokDJwLwzHfPYCuXgw6XMjLMGE+t4ZprYP16S8Ko\nNRmsDpkM5nsBSzqVUr2AX4DrgRXAs8BmYAzwnVKqjb+2o5TKAJYBZwP/BZ4HYoHngBkNPN1sYJKL\n00+exCpESJg6Ff7zH4iPh9mzpQC8h/bF7oMjd8DhjpB/eo1bZgHXk58/XMaHRaiLjr6IU5JPYWfR\nTl75+RWrwwkqtWaIP/ggXHklHDpkktD9+wMeT+3JYLUiJSOjSCaD+Vgg17N7GWgPjNZav+S8Uik1\nFbgTeBwY5evtKKWSgFeBCmCg1nql4/qHgCXAlUqpq7TWH9V5Hg3M1lpP9/aFChEyPvnElEcCs06y\nTBzy2KJti8yFDUNAO4/fbUAL3I0PmzLFJj9iEUApxcMDHybjgwye+vYp/nnKP2kR28LqsCxVUVHB\n+PGzmDOnFbm5PejRYxkZGYfJfO01YjZsgNWr4bLLTAH5+MCWHsvMvAyYxZw5LcnLS6F7921kZBQ5\nrhe+FJCWTkfr5AVATs1E0WEiUARcp5Rq8FvZxO2MwCSpM5wJJ4DWugx4EFDArd6/quAm9cZEo1as\ngL/9zVx+4glTO094bN4GM2v94j6dSE1dQHT0Orp2nQHI+DABl/S5hH6d+/HH4T947ZfXrA7HxpGD\njQAAIABJREFUcm5niE/8AubNgy5dTG3gv/894Etl1pwMlp2dwLp16UybNoKYmEC2y0WGQHWvn+c4\n/6LuDVrrw8C3mKaBM/2wnfMwrZYLXWzva0zTxAClVGyd2xRwsmPc571Kqb8ppbo2Ep/lpN6Y8MiW\nLWZZy5ISuOkmuPdeqyMKKX8c/oPv878nISaBDx6fWPVj9euvGaSmbnf5GBkfFlmUUjx8rqnb+eS3\nT1JcXmxxRNZpdIZ4+/awYAEkJcFHH1X3vgSYczKY9Eb4T6CSzr6YxG+Dm9s3Os77+GE7fR3n9R6j\nta4EtmKGGfRysb07MGNGpwDTgRyl1MtKqaBddkTqjYUPv7VW798Pw4bB7t0weLDMVG+CTzd8CsD5\nPc+nZVzLqh+r9u3by/gwUSXjmAz6de7HjsIdTP3fVKvDsYxHM8RPOglmzTKLUjz7LEybFuAoRSAE\nKuls7Tg/6OZ25/WNzWJvynaa8pitwO2YhLUl0AXTTb8V+CfweiNxWkLqjYUHv7ZW22xmwP7vv8Px\nx5tWhdi6jfyiMc6u9eF9h9e7rWax8OjodaSmLmDMmPkyPiwCRakonh38LABPfPME2w+5bgUPdx7P\nED//fHjzTXN53DizfxJhRep0uqC1/lpr/ZLWepPWukRrvVNr/QkwCNgP/FUpdYK7xy9duhSllNuT\nv0i9sfDgt9bqsjK44gpYvhy6djW18Vq3bvxxohZbuY1Fm80koov7XFzvdhkfJmo6r+d5XHHsFdjK\nbdz35X1Wh2MJr2aIX3stPPmkKaV03XVmnKdoNityElcCtRd0tia6+4VzXn/AD9vx1XOjtd6ulFoA\nXAOcC6xp7DGuLF26tCkPa1R5eTnDh+dw4MDuercdeeRGtmxJJS8vzy/PHU5ycnL89hk1pry8nJyc\nA6Sn/1Dvtm3bDrBo0SJim9IyabebmeolJXDRRWbFoS1bzCmMBOKzy96TzRkVZ9ClVRc2/LyBDW5H\n+xjynfOcld89f7o26VoOqAPkr8nnneh36N46PMuSNfT5DR/ejoSEN8nOjuPgwda0bn2Qvn3LGDz4\n2PqPOf10M67zxx/NJMf8fDPRSIS8QCWd2ZiJOe7GbB7tOG9479207WQDpzges7LmnZVS0UBPTDkl\nT399nRldS3d3SE9PZ8mSJR5uzrfmz5/J7NmnU7uL3caYMbu54IILLIkp1CxdupT09HRLnnvz5s3M\nm9cFuz2t3m3R0R3IzEygd+/e3m3UbjeThd5807RsLlkCJ5/so4iDSyA+u/fnvc9SljL51MmkD/Tv\nc0UaK797/vZz/M88vvxxDu86zPfDvyeq/rokIa+xz2/QoEHYbDYKCgpITk5ueIzzuefCX/4CH39s\nks+vvjLjPkWT6AbWuA9ka2eg/uqdGdjgujcopVoBZ2Ha3Vf4YTtfYRLVIS62NxCTnX2rtS5v5Lmd\nznCcB2UTkYwnC20+Xx1Da7jzTpNwJiaaLvUwTTgDwa7tVeM5L+l7SSP3FqLafWffR5ekLvy04yem\nr4rc8s8ezxCPjob33oNLLoF9++CCC+C33wITpPCbgCSdWustmDJHqUqp2+vcPBnTajhda10MoJSK\nUUr1ddTlbPJ2HD4G9gB/UUqd4rzSMQP9Mcxs+Jdrbqjm/Wpcp5RSE4D+mNbOzz168QEm48lCm89X\nx5g4Ef7v/yAuzswMPessX4UakX7a8RN/HP6D7kd056RO0uoiPNcqrhVP/fkpACYsnkBhaaHFEYWA\nuDiYORMuvNBU2zj/fNjQWIeoCGaBzERGYepoZimlzgfWY+pppgO/Ywq1O3V13J5D/VJG3mwHrXWh\nUupmYCawVCn1AbAPGI7pcp+ptZ5Z5zl+VEqtBVYB+Zhxn2cBx2MK0F/rqAsatJxHkyL0+GR1DK3h\nscfg0UdNi8EHH5jySKJZ5mU7Wjn7XBLwAfgi9F1zwjW8+OOLrNi+gkeWPMKtR9/aeDdzpIuPNwfM\nF19sutgHDYKvv4ZerqocimAXsEEljlbKU4G3gNOBcZjxlM8B/bXWdRdd1Y5Tc7eD1noOpit9GXA5\nphxSGWbZzL+6CPcZYC+msPwdwHWYBP154ASt9WKPX7gQXmp2a7XW8MAD8PDDEBUFb71llpcTLnla\nD1VrzcfrPwaka100TZSKYuqfTb3Oqd9lcfQZG2QBD0+0aAFz58I555hJRYMGwbZtVkclmiCgfa5a\n63zgRg/utw2Ibu526jzmf0D9+iau7yvLswjLNam12jmGMyurekzU1Vf7J8AQ53Yt6MzLXCb43+Z9\ny+97fqdTy06c3/N8CyIW4eCj5/Jh2zXQ7330kOfJeW8+WVnFwCymTRthdXjBq2VLMyZ98GCzhO+5\n58KiRdCnsTVlRDAJv+lzQkQqux1uvdUknHFxpkSSJJxueVsP9ZWfXwHgHyf/g9hoKagvvFe1gMeX\nmVB8JBz9GZz8BoFYwMNvK5wFUlISfPYZ9O8Pubmm5fPXX62OqpaweJ/9SJJOEbHCaudQUWFqb/7n\nP5CQAHPmmJWHhEvert61r3gfH60zq6Pc9KebAhOkCDtVC3gcToYFL5grh4yFI7f6bQEPv65wZoUj\njzQtnIMHw65dkJ4O335rdVQ+fZ/D6repDkk6RcQJu51waSlccw1Mn266oBYsgCGuKoQJJ29X73p3\n9buUVpZyQa8L6NVGJjCIpqlVEm3NNfDbFRB/GC69gW7dt3pfEs0DflvhzEotW5oxnldeCQcPmnJK\nn1tbUMYX73PY/Ta5IEmniDhhtRN21q+bOROOOAIWLoTzzrM6qqDnTT1UrTWv/vIqALeccktA4hPh\nqXZJNAWfvgyHO0LqMnpcNdPns9i9bdEPKfHxpirHjTdCcTEMH27ZWu2+ep/D6rfJDUk6RUQJq53w\nli0wYED1Wupffy11OD3kTT3UFdtXsHbXWjq27MjwvsMDGqcIP7UW8CjdRcfv/wnAD0kfsn73ep8+\nl7ct+iEnOhpefRXuugvKy80KRs89ZyZUBpAv3uew+m1qgCSdIqKEzU74hx/gzDMhOxtOPNHM5pQl\n4rzi6epdr/xiJhCNPGkkcdFxVoQqwkjdkmhbP7+PG/rdQGllKX/779/4fePvPkswfL7CWTBSCp55\nBqZMMcnmuHHwr3+ZJDRAfPE+h81vUyMk6RQRJSx2wrNnm8Hzu3ebwfTLl0O3blZHFXI8qYd6oOQA\nH679EJAJRMK3ai4HmfnnTJIq2/PLH79w3C0v+Gwsn89XOAtWSsGECfDhh2Yi5SuvmHHt++uV7fYL\nX7zPYfHb5AFJOkVECemdsNaQmQmXX27GMN14I3z6qRnLKZqsobWg31v9HsUVxQzqOYij2x1tQXQi\nEkx+YDGF75j12PU5/yGnvK3PxvJ52qLviaCfVX3VVbBsGXTqZFYvOvNM2LgxIE/d3Pc5pH+bvKG1\nlpMPT4BOT0/XIniVl5frMWM+0qmp83V09FqdmjpfjxnzkS4vL9daa71kyRJrA3Tl0CGtr7xSa5N6\nav3oo1rb7VZHFXR8+dnZ7XZ94ssnaiahP1jzgc+2K9wLyu+enxUVFemUlPnmq33hWM0kNHcla5Ly\ndWrqfF1UVOSz59m0aVOTtle9z1ygo6LW6tTUBbX2mU5B8/lt26b1iSeafWWbNlovXhywp/bN++z6\nt8lfcKwAqQORIwXiSSLpJEln6HC3cwiaHafTb79pfcwx5ut6xBFaz5pldURBy5ef3ffbv9dMQrd/\nur0uKS/x2XaFe0H33QuATZs26aiotSbpjC7VjDzXJJ43n6aj4n/SmzZtsjpEPWbMRxqKqo55zalI\njxnzUa37BdXnd+iQ1pdcYoKNitJ6yhStKyutjsojzUlcmyKQSad0r4uI1VC3atCYORNOPx1+/x3S\n0uDHH+HSS62OKiI4VyAaedJI4mPigRDoXhQhp9ZYvso4+Ohj2J8KXX+kxVV307lzZ0vjC9lZ1UlJ\nMGuWGetpt8P998PFF8OePVZH1qiQ+G1qIkk6hQhG5eVw991mjNLhw6YUyPffyzrDAXKo9BAz1s4A\n4OZTbo6Ios3CGvXG8tk6wAdzoKwlRb2X8NKvL/n1+Rs7kArpWdXR0WZW+/z50LatWULz5JPhu++s\njixiSdIpRLBZv96sLZyZCTExZi319983q3CIgHhj5RvYym0MTBlIn3Z9IqJos7BOvUkoLbYzrOxW\nAO798l4WbFzg8bY8bY339EAqLGZVX3SRWaO9f3/Yvh0GDjT7Vx3Yep5Ckk4hgofW8MIL8Kc/wc8/\nQ0oKLF0Kd9xhSoKIgDhQcoDHvn4MgDvPvDN0uxdFUPAkCXRVvuvTZ55hcvpkNJq/fvxXFv6ysMFt\neNsa7+mBVNjMqu7e3cxsv+suqKgwPUkXXgh5eVZHFlEk6RQiGOzYAUOHwujRUFIC118Pq1fLCkM+\n5GkL0FPfPMXe4r2c3eNshvcdHtrdi8IyTRmSUXcs330D7uPosjM5VHaIIW/fRN/TPnG7DW9a4709\nkPJl2SVLxcaaFs45c6BdO1i0CI4/Ht54Q1o9A0SSTiGspLUpaHzCCWbd9LZt4eOP4a23pP6mj3jz\n4593MI9p308DIPOCTJRS4dG9KALOF0My7r57NhufmQs7ToG229l+/qNkvXFyvW14m0R6eyDlyUIK\nzRHwCXrDh8PatZCRAYcOmZrHw4ZBfr7fnlImIRqSdAqvyZfHR7ZsMTu6v/wF9u0zXT1r1sAVV1gd\nWVjx5sf/wSUPUlJRwlVpV3FGtzOAMOpeFAHjiyEZVdso7wDvfAEFJ0O7jTDyIj75oqTWNrxNIpt6\nIOXrWdWWTtDr3NnMbn/3XWjTxkwySkuDt9/2aaunTEKsIxB1mSLpRBjX6fS0QHCo83utudJSUzMu\nIcHUkGvdWut//1uKvftA3c+uVuHtOqe6hbdXFqzUapLSsZNj9eZ9m2ttx6qizZEmqOo8NkOt2pt1\nTtHRaz2qvVlvGy32av7Zz9TwHJ2iv139bdV9i4qKdGrqAo/+zp08rb3pDW8/P3/E0CT5+VoPG1Yd\nxMCBWq9Z45NNB81rbABSp1MEI5nB6wPLl5uSHfffb8ZuXnONqcH5z3/KZCE/8LQFSGvN3YvuRqO5\n7bTb6NWmV637+rt7UYQXXwzJqLeN4rYw/Uso6AfttjFyyUh2FO4AmtYab/U4zaCaoNelC8ybZ4Y1\ntW9vJhz16wdjx8LBg03ebFC9xiAhSafwiHx5mmnrVpNgnnsu/PYbHHWUGcT+3numm0f4hac//l9s\n/oIvt3xJ6/jWPHjug4DrYSThXLRZ+I4vhmS43EZxO5g+l/YVKWzcv5Hz3j6vKvH0Nom0+kDK1xP0\nmj3sSykzgTM7G267zTRIZmWZ2shvv20KzHtJJiHWJ0mn8Ih8eZpo714YNw769oUZMyA+Hh5+2Izd\n/POfrY6uFl+M1Q228b6e/PhX2iu5e9HdANx/zv20jmstY7BEs/miJdHlNm5ZwZq7V3BSp5PYsHcD\nZ7x2Bj/v+LnJSaRVB1K+mqDn8zGTbdua0nU//2yqh+zaBSNHwplnwpdferUpmYToQiD68CPphA/G\ndAZ63VVPNGXMUKjyybgym03rp54y4zVBa6W0vu46rXNymr/tZqr79+WLsbrBMt7X1WfX2HjMN355\nQzMJ3eO5Hrq4vDgkxmCFq3AZ01mTL/bnrraxu2i3HvD6AM0kdMJjCfr91e/7ItxmsWJMp1+/r3a7\n1tOna925c/XGBw3S+n//C474msm5bySAYzotT9LC7dScpDNYfrjdCaYvjz8T82b98NlsWv/f/2nd\nrVv1m3TBBVqvXOmz+JrK3d/X6NEfBPeOvwF1/w4a+uxc/c3sKdqju0ztopmEfmfVO15NPBK+F45J\npz+VlJfoG+fcaCYXTULfu+heXVFZYVk83n5+zZ2gF7Dv6+HDWj/xhNZHHln9BBkZWq9e3ehDg3kS\nYvV+W5LOkD01J+kMpqTOlWD48gQiMW/SD9/Bg2an1LFj9Yd30klaL1zos7iay/Xf126dlPRhs3ba\nViRq7v4OFi9e7Pk2Ksv1BdMv0ExCn/HqGbrSXumTWcei6STp9J7dbtcvfP+Cjn4kWjMJfdF7F+kD\nxQcsiaWpn19TGxEC/n3dt0/r++/XOjFRV/VgXXaZRy2fwdaDWXu/LUlnyJ6amnSGUgtLoL88NZ8v\nEIm5VzvO3bu1fuih2kfAp56q9axZWldW+iym5nL/97VJw+pm7bStSNTc/R3ce+8LHm9j/MLxmkno\njs901LkHcrXWkTWMJBhJ0tl0X235Srd7qp1mErrP8330j/k/BjyGQH9+ln1f//hD6zvu0DourvoJ\nzz5b67lzg2q/35Da+20pmRRxQmmiTqAGntcdIH7ssQt54w1NUMyg/+EHM9OxWzd49FE4cMDMTF+4\n0Nx26aUQFTxfL/d/X8nAFpePaXJplyZswxsNVVLIzo7z6O9gxpoZZP4vk5ioGGaOmEn31t3NFqQQ\nvAhR5/U8jx9v/pETOp5QNcHo3kX3UlxebHVofmPZ97VTJzOzPScHJkyA1q3hm2/MSkfHHw+vvQZF\nRf55bh9paL/tT8HzqxjhZJZbfXXrgubmnkhh4XEu7xuQxLy42NRxO+00OOMMmD4dysrMqkLLl5va\nboMHB2W9Tfd/X4kkJWXj89IuXm7DGw0doB082LrRv4Nf//iVG+feCMC0C6dxbsq5tW63un6hEE3V\ns01PVty0gnFnjgPg6e+ept9/+vFN7jcWR+Y/ln5fk5NhyhTIy4NnnzWNEOvXw803m9qft90Gq1b5\nP44mcL/f9rNANKdG0okwHtMZSK67g4s0+L8rpVYXkd2u9YoVWt92m9Zt21Y/Ydu2Wo8fr/XmzW63\nE2zc/X2NHj2j2WN1/T3et+YQi4a61C699JUG/w52F+3WKc+laCahb5h9g7Y3sApUsI3BigTSve47\nK/JW6ONePE4zCa0mKX37/Nt1YWmhX5/Tys8vKL6vZWVav/OO1v37194xnX661q+/rnWhf9//mjx5\nP2T2ehicmpN0BsNEHSvV/JK4HycYoDGdW7ZoPXmy1n361A7glFO0fuMNM0s9xDT29+Wv0i6+idmz\nGfcNjeksryzXg94epJmEPv3V03VxebFPYhS+I0mnb5WUl+gHFz+oYybHaCahu0ztol/64SVdWlHq\nl+cLxs/PsmR09Wqtb7+9umweaN2ihdZXXWXG/JeU+OVpmzLZVpLOED41J+l0CoojtgDG4epLMmrU\nO24mvpTrpKSndErKPN8n5hs3av3MM3rJddfVftJOnbS+806tf/45LNZHD5a/L0942zrrbvZ6aUWp\nvn7W9ZpJ6E7PdNJ5B/MC/EqEJ4IxaQkHKwtW6lNfObWqtFLqtFT95so3dXmlbxs0gunzC5oShEVF\nWr/1lploVHNH1rq11iNHav3551qX+u4goCk9ppJ0hvDJF0mn1Xz5ZfUkwXH3JenX7zG3Xx6fJE52\nu9Y//qj1Aw9onZZW9SRL0tNNSYxrr9X6s8+0jpCW5mDjSUUHT+p0FhQW1CqivXzb8gC/EuGpYEpa\nwo3dbtcfr/tYH/vCsVXJZ9/n++oP1nzgs9qewfT5BeVwtZwcs2hIv361d2hJSVpfeaVJTnftavLm\nm1oFR5LOED6FQ9LZlC9rU1e5aehLkpIyV48a9Z5vhxvk5Wn95ptaX3NN7ZqaziPPa6/VS158MaBj\nb4RrTSnFVPdH78f8H3XXqV01k9Ddnu2mf8r/KUDRi6YIpqQlXFVUVujpv07XvbJ61Wr5nPL1FP1H\n4R/N2nawfH4hUYJw/XqtJ06s1eChwdT+7N/fDO/65huvWkGbWr5Oks4QPoV60untl7W5q9x48iVp\nVqtmXp7WH35oxtYcc0z9J+naVetRo7T+4ouqL7cVteY8fX2h1DXeXE2pwef87IqKinTmF5k64bEE\nzST0Wa+f1ewfVOF/wZK0RIKyijL9n5/+o1OnpVYln7GTY/XVM6/Wn63/TG/cuNHr/UywfH4ht8jD\nli1aP/+81hdeWLv2J5het8GDtX7ySa2//95MVnKjqXVLwzbpBLoCbwD5QAmwFXgOONLf2wEGAAuA\nvZgaAauAMUBUA4+5HvgeKAQOAEuAYY3EFtJJp7df1uaucuPT4r7Fxaa7/Pnntf7LX7Tu0aP+Rlu1\n0vrii7XOytL6t99cjtEM1I7Tm2EMQTM+KcC8bXVfvHixvm3Mu/qIKy+r+iE9fsKfdVFJ+Cfp4SBY\nkpZIUmmv1J9t/ExnzMjQUY9EVX1vGJ2iW18+Ql897nFdWuZZa1uwfH4hvchDYaHW//2vaQw59tj6\nL6BFCzM+dPx4rT/+2DSs1CBjOquTsV7ATqAS+ASYAnwJ2IHfgDb+2g6QAZQDh4BXgacc97UDH7p5\nnkzH7duAqcDzwG7HdaMaiC+kk05vvqy+WuWmSWNv9u/Xevlys875yJFan3ii1jEx9Z+wdWuthwwx\nXRXLlzd4lOgUqB2nN687KMcnBYA3FR2Ky4v1yAfu1IxLNj+aD8VoTn05It6ncBEsSUuk+sfYlzXp\n92vGdalOPiehWz7cRt/66a164aaFuqTc/azrYPr8wmafWVCg9YwZWt98s9ZHH13/Nw607tJF64su\n0nrCBF3x3nv68eue071S5no8LC1ck86FjkRxVJ3rpzoSuZf8sR0gCdgFFAMn17g+DvjWsa2r6jym\nv2Nb2cARNa7vAexxtJT2cBNfSCedWnv+ZXXfKlqkYbbHR5luE4vSUq23b9d66VKt//1vs+zYn/9s\nvmCuNh4VZY4Mr7vO3H/NmiYtSRaIHac3wxhCYnySnzU0rKC4vFg///3zOjkzWadPSjc/lP86SdNj\necS9T6EumJKWSFNrPxNVrkn9SjPkDs2d3WsloAmPJeiBbw7UD331kP5i0xe1an8G0+cXtiUI9+zR\nesECrR9+WOvBg7W9ZkmmGid7ixa6JC1Nl191lWl0+fBDrVetclnuL5BJpzLP519KqV7AJmCr1rp3\nndtaAc4lRDpqrd2u2dWU7Sil/gG8Bryltf5HncecBywGlmmtz6tx/XTgWuAGrfX0Oo95BHgQmKy1\nfsRFjDo9PZ0lS5a4exlBr6KigvHjZzFnTkvy8lLo3n0bGRlFZGZeRkxMTNX9bDYbaWnLyMkZWm8b\nSUlPU1h4O7WXKrQxZsx8pk0bYf6rNezZA7m5kJdH2aZN2H77jVa7dhGzdSts2QIlJa6DTEiAY4+F\nk0+GP/3JnE48EVq2bPbrX7p0Kenp6fWut9lsFBQUkJyc3OxVdjZv3kyfPiXY7Wn1bouOXkd2dgK9\ne/f2+r6RQmtN9t5s5mbP5f++/z/yC/MBSD98BUs/vRayM0BXL7gWqe9TqHH33RP+534/o4nq+jG3\nZi3j611fs2bXmlq3RqtoTk4+mT91/hNHHTqK/uf054SOJ9A6oXXggm+AL/fbwcT5Oz13diKxuYrz\n239LRs/fuaBjGVGrVplVktzp2hV69qw6qcmTAdBa+305vZjG7+ITzoTui7o3aK0PK6W+BS4AzsSM\nm/Tlds7DZPELXWzva0yr5QClVKzWurzO87h6zGfAQ8AgoF7SGQ5iYmKYNm0EU6Y4v6zpLr+szmW0\nsrJsVCeXmpbsZtzlLUgq/T/WfFVG1O5o+rbeyJmpuzhnRys493koKIDt22sllXGOUy0dOkDv3nDM\nMXDcceZ07LGQkgLR0R6/pubseKqT8Fbk5vagR49lZGQcrpeEe8MsS7mMnJz6iaRZ9jS9SfcNZ6UV\npSzbtoz5G+Yzf+N8Nu/fXHXbiZ1OZMKZE/jgkUPwe/3l7yLpfRKiKdzvZxQ9Ylvy9NCnSUxMZI9t\nD9/mfsvX275mee5yfin4hZ92/MRPO34inXTu2XQPACmtU+jVqhfHdDqGYzoeQ+82vendtjepR6aS\nEJPgUUy+SBgTExPD8mDTuUy087d3w+6LeHm3o2Fn3gjYv98syfn775CdXX2+aRPk55vTN4FfHjVQ\nSWdfTOK3wc3tGzHJYh8aTjqbsp2+jvN6j9FaVyqltgLHYcaKZiulEjETlQq11jvdPAeO5wgvFRVQ\nVFR1Siwqovfhw+YPtbAQDh2qPj9wAPbv59n9+xndZSLlu4tpVV5MB/YRTzm8XWfbB4BfHaea2rSB\n7t3NqUcPk0z27l19OuKIZr6k5ieMdb/cOTlpjkR7VnWrrZdcJ+zgar1yb+4bDrTWbD+0nd92/1Z9\n2vMbq/5YRVF5UdX92rVox9CjhzLiuBFc3OdiolQUv/Z9kTlExvskhC95up9pn9iejGMyyDgmA4DC\n0kJ+3PEjq3euZtuv2zioDrK6YC3bDm5j28FtLMmv/ZOuUHRo2YEuSV3oktSF5FbJdEnqQudWnWnX\noh3tEtvROq41L0/9icWfdiJvSx9SfHCgH05sNhuzZ7ek9ucEkMicOS2ZMsVGYps2MGCAOdVUUWFa\nQbduNactW8z68QESqE/P2c5+0M3tzuuP9MN2vH2MT2ItW7MK7PaGT5WVoB3nlZVQaUfZa/y/oqL+\neUUFlFegysuhsgLKy6tPZeZclZVBWRmUlkJZKZSay6q01FxXXAIlxaiSEnO5uBhsNvM4L0UBdY8h\ndYsW0KE9ul17aNcW3bEjOjkZOnVCJ3dGd+4EnTqju3eDVq0afoKKUq9jqumu8Z/w4gtDgURQkJN3\nFFkv2KjgI6ZmXuH6Ke0VlDqe12azMWtunKNVtWYs0cyeF8fEyfubnMw8/uRFVDCbT+e1JG97D7p3\ny+XiS4p4/MmMqudvyn1r0rgePuNqWE3N+9a8XeMYj1Pn3K7tVadKXWnO7ZVU2Csoqyyj3F5OeWU5\nZZVllFWWUVReRFFZUa3zAyUH2FW0q+q0s2gnOw/vpLjC9SibEzudyMVHX8ywPsM4o+sZREfVbu0e\nPPhYSkrmuxwaIoRomPmeuB5a5U5SfBKDeg5iUM9BLC1Zip49gJXPXwjttkP736HNZmjIammSAAAX\nc0lEQVSzgR79fiCm42G2HdhW9X3/9Y+6rRA1HAn8DaiMIacsiazSVrw7+S76pHQjKT6JlrEtSYxN\npEVMC3Me24IWMS2Ij4knPjqe+Jh44qLjiI8257HRscRExRAbFUtsdCyxUbFER0UTraKJjoomJiqm\n6nKUiiJamfMoFUV0VDQKRZSKQilV73JD52ASbaDR/9flvL3WdSi25m0lt6ATxBTXugUgd0dncrbn\n0KtXL/fvbfdkczrXkZAGMOkM1JjO/wA3ATdrrd9wcftjwATgfq31U77cjlIqGzgKOFprvcXFY77B\nTBwaoLX+XimVjCnFtF1r3cPF/WOAMqBUa93Cxe2NvqH+f8ebplJBUSwUxVWfH46DQ/FQ6Dx3XN7f\nAg4kwP4Ex7nj/7sTobheH3loSSedpSy1OoyI1iGxA8d1OK7WKa1DGp1adWrwcc4xgeE6jivcyZjO\n4NDU78+iRYu4+eZytm27qN5tqakLWLcunbiEOHYV7WJH4Q4KCgvM+eECCgoL2Feyj12Hd/G/X/Mo\njymDFnsh1s24fuGdSY3fJZzGdDpbB92NLHZef8AP2/H2Mb6K1a33hqebqWLKJKB2VX1ZK8f/Hdfb\nlXKcm9sqnedRVF1vd/y/UoHdcV7puK4iCiqjVNXlCuU4jzbn5Y7L5Y7H4eLIqjExQAfH6eimvil+\noLXGbgdcHkVqoqJcH0n20D2IVtUtaJWV2u02oqPdv19a63rbd3WdVdwdXVfdXidOV0fnSjmO+Gsc\n3ddsKah5OTY61rQ4RJlz56lVXCtaxrWkZWzLqvP4mPjqJ7YB22D9tvWsZ32DMefk5LB06dKq/+c1\nNJheBJ26n5+wlrffn02bNtGrVzt69lxa7zalDvP555/Ttm3bquuSSKKv4x9JQBLsi95H9JoKtO7o\neGAFxJRBdCkq5g8uv6qS+MT4qp6UCntFrcuV9koqtDmvedlVr4zG9NjU7Llx26Njt6OizL7P2Vjn\nvI/zct3baqrbwOeuF8rd/euqtNvRdsdkyRptXUppoqLq79sXs7jB7QVMIKbIAzdiShC97Ob2zzGl\ni87z9XaAdxzXXe3i/tHAYUy/aWyN6/Mcj+nk4jFnOmJY5iaGWiWTIrWot1VqltZpaoHgumU/vKn3\n5urzHj16hh49+gNL/gYiaQUjrYOrZIvwnnx+oe2LL75odlH2YCrsHsy/396WhGrod4xwq9OJmaRj\nBza7uK0VZsWfQqCFr7cD3OB4zJsuHjPIcdtXda5/25F0Xu/iMZMdj3nYTYw6PT296osRNgVqg1xz\nl+Os6YsvvnCzjnzjX27Xn/d7Af8bCOadpT9J0hLa5PMLPTUPbJcsWeKT37xg+d0Mljga4knDQmO1\nnsMu6dS6Vivk7XWuf9aRxL1Y47oYzKzzXs3ZjuP6msXhT6lxfTzwnWNbI+o8xlkcfgM1ltYEUqle\nRrPB4vCpqQv0qFHv6JSUT/16xBZpLVnuuNs5jB49w+OE0ZmoXXrpKy4Ttcbea9df7CINgS/sHgo7\nS3+QpCW0yecXOlwd2N577wu6uLi42UXZg6GwezgtytHY8tbhmnT2whRvrwRmYZav/AoXy1cCKY7r\ntzRnOzUek4GZ/FNI9TKY6x3b+MBNvJmO23MdCe0LmGUwK4FbG3idOj093fGBrtHeLAfpjUhtyXLF\nk52DJ8m5M1FLT1/icaJWc7uuv9ibNHi+ln1z3oOawwrCZWfpLUlaQpt8fqHD1YFtevoXVftLXzSI\nuNtGIBpbGkvUfLHvDlSjUWNDFgKZdFYv2eFn2swcPxV4CzgdGAf0BJ4D+mut99d9iOPU3O2gtZ4D\nDASWAZcDt2OS0DuBv7qJdzyma74AuBm4DlgDXKy1ftmzV92L6GjXJUVNsepkzzbjgrN2ZE7OUOz2\nNHJyhpKVNYzx42c1eZuhqqCggLy8FJe35eWlUFBQUFUg2N1MzMbqntlstlrXVlRUMHbsTNLSltGn\nTwlpact49tn/0b37tjqPT8Yct9TX3L8Bd3GMGvU6eXn1Ci8A1e+HEEI0lfv9ZWzV/rKxfa4n6m7D\n1f5u7NiZVFRUNP3FuGGK5ftn3x3I1wHVNVhNJ21NpgZrQAUis42kE7VaOrWGl3zezdmclixXR1ah\n3kXvi4HnNY9qa7d0uj6qddd93a/fYy6u99+YTtdx7NZJSR8FfUunP/7upKUstMnnFxrctQKmpy/x\naQ9OXb4cNuRN75ev991WDH9qaMgC4djSGalSUroxatRsUlMXEB29jtTUBYwZM79Zxao9admry9WR\n1R13fMAdd3wYsKMtf2nsKM6TI21vjmobahXdv//Eep/36NFRjB49z6d/Aw3H0R7YSnPeD38K9FG+\nEMK3/NkK6I63vVHueLP/ycy8jDFj5vt03+2r1+Et5/LW69alk52dwLp16UybNiLwKzwFIrONpBO1\nWjqLfDq+xakpLXvBMqvaX3wx8NzTMZ2ejPUJRItyQ3FERf2qR458xdKB+O748yhfWspCm3x+oaOx\nMZ2+5qsxlk3Z//hy3x2IsaLeIoAtnZYnaeF2ciad/v6R9+aLE0yzqv2tOTuHmrPXG0rUgqWOnCdx\nBNvQCV9N+nJHkpbQJp+fd6z8frs60L/33hf89pvni/1uMEyyDJbfj5oCmXRK97qf+Lvp2ptmf9fd\n8QWYIgH1hfJkk+YMXnd2P4waldpg94MvuvN9wZM4fDGY35caGhqSm9uV2257T7rdhWhEMAxRcdVd\nO2RImt9+83yx323K0DRfa87rsNlsbN682W9d8AERiMw2kk5Qe0Uif/O0MGz9I6siDcF1tBUsPGlt\nCYY6csEUR0M8XSUqKempZne7S0tZaJPPzzPBWofX359fc/d3wdLK6O3r8HeJRKR7PXRPgU46PRXu\nYzp9yZsdZ7B0X/szjqZu27tVonbrpKQPm/1jIElLaJPPr3HB0EXsTqA+v+bs74IpYff0dfg75kAm\nnQGetiSsYrrdZzFnTkvy8lLo3n0bl1wSBcxj3rykqusyMoqaPas6kji7r63mjzgqKioYP34Wc+a0\nIje3Bz16LCMj4zCZmZd51IXmrCXrnKWZk5NGVpaN0aPnMmbM/Fp/iwMHbuadd85zuR1nt1cwvM9C\nWM2TLuJw/640Z3/n6rfQqt89T15HY7Pdp0yxBc3wKU9I0hkhnONvpkyxUVBQQHJyetUf6pNP1r9O\nCHdJI8xi2rQRDT62oR3lvHlHsG5dOlOmUPV3B+ksW7aMnJzj623LlGBJb/4LEiIMmHJFy8jJSat3\nm3xXGtfQb2EwCreDDJlIZCErBgW7mlgSbJNNhPWaW0vO21WigmVylhDBTr4rvhEqv3tW1ET1J0k6\nLRAMMw+FaEhzZ3k2ZUfpj0LMQoQj+a5EjnA7yJDudQs0p9tSiEBobheec0dp/q5r7hTd7yhDrdtL\nCKvIdyWyBNM41OaSpDPAwm1QsAhPTUka62rqjjJYJmcJEezkuxIZwukgQ5LOAAu3QcEifDX36Dqc\ndpRCCGG1cDjIkKQzwGTmoQgVvkoaw2FHKYQQovlkIlGAhdugYBH+QmWWpxBCiOAmLZ0WCKdBwUII\nIYQQnpCk0wIy1k0IIYQQkUa61y0k3ZYiVFmxsIEQQojQJkmnEMJjsrCBEEKIppLudSGEx2RhAyGE\nEE0lLZ1CCI80dz12IYQQkU2STiGER5q7HrsQQojIJkmnEMIjZmGDXJe3mYUNkgMckRBCiFAiSacI\nOJn5HJpkYQMhhBDNIROJRMBUVFQwfvws5sxpRW5uD3r0WEZGxmEyMy8jJkb+FEOBLGwghBCiqeSX\nXgSMzHwOfbKwgRBCiKaS7nUREDLzObzIwgZCCCG8JUlnCAnlsZAy81kIIYSIbJJ0hoBwWAVGZj4L\nIYQQkU2SzhDgHAuZkzMUuz2NnJyhZGUNY/z4WVaH5jGZ+SyEEEJENplIFOQaGws5ZYotZBI2mfks\nhBBCRC5JOoOcJ2Mhe/fuHeComkZmPgshhBCRS7rXg1w4joWUmc9CCCFE5AlY0qmUGqCUWqCU2quU\nsimlVimlxiilvI6hKdtSSl2vlPpeKVWolDqglFqilBrm5r5vKqXsbk6VSqk+DcW3dOlSb1+SWzIW\nMrCUUpx33nlWhyGaQD670CafX2iTz094IiDd60qpDOBjoBj4ENgHXAI8BwwArvbntpRSmcA4IA94\nBYgD/gLMU0rdrrV+ycVTaWAacNDF9Xs8jdcXZCykEEIIIUKd0lr79wmUSgI2A0nAAK31Ssf1ccAS\n4Ezgr1rrj/yxLaVUf+BbYCNwmtb6kOP6HsAvmBk6x2itc2s85k3g70DPmtd7+Ho1gD/eV5vNORYy\nWVo4/UQpBfjn8xP+JZ9daJPPL7TJ5xe6anx2yt/PFYju9RFAe2CGM0kE0FqXAQ8CCrjVj9u6FdM6\n+bgz4XQ8Jhd4EYgHbvDyNVlCxkIKIYQQ1gvlxVqsFIik8zxM0rfQxW1fYwYrDlBKxfppW85BJq4e\n8xkmUR3k5vkuUkrdo5S6SymV4WhpFUIIIUQECofFWqwUiDGdfR3nG+reoLWuVEptBY4DegHZvtyW\nUioR6AoUaq13utjeRse5u4lBL9a4rIBCpdQEN2NAhRBCCBHGnIu1OGtn5+SkkZVlA2YxbdoIS2ML\nBYFo6WztOK87IYc61x/ph2019bmXYSYkpQAtgN7AXZhW1ueVUjd5EKsQQgghwkRji7VIV3vjPGrp\nVErlAD282O67Wuu/NymiIKC1fqvOVTnAc0qpDcA84HGl1Ou6gRHTzoG5IjTJ5xe65LMLbfL5hbZI\n/fxycqBlS6ujCH6edq9vpH6hyIbsqHHZ2ZrY2tUda1x/wIPterstXz43Wuv5Sql8oAumG3+dJ48T\nQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fit to skewed distribution\n", "sopt, scov = curve_fit(skewed, x, yn, p0=(20, 20, 1, 1))\n", "y_fit= skewed(x, *sopt)\n", "\n", "# fit to normal distribution\n", "gopt, gcov = curve_fit(normpdf, x, yn, p0=(20, 20))\n", "y_gfit = normpdf(x, *gopt)\n", "\n", "# plot\n", "#plt.plot(x, y, \"r-\")\n", "plt.plot(x, yn, \"bo\", label=\"data\")\n", "plt.plot(x, y_fit, \"g\", label=\"fit skewed\")\n", "plt.plot(x, y_gfit, \"r\", label=\"fit normal\")\n", "plt.legend(loc=\"upper left\", fontsize=16)\n", "\n", "# parameters\n", "print(\"Parameters skewed :\")\n", "print(\"-------------------\")\n", "print(\"mu :\", sopt[0])\n", "print(\"sigma :\", sopt[1])\n", "print(\"alpha :\", sopt[2])\n", "print(\"a :\", sopt[3])\n", "print(\"\\nParameters normal :\")\n", "print(\"-------------------\")\n", "print(\"mu :\", gopt[0])\n", "print(\"sigma :\", gopt[1])" ] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }