{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 4: Continuous random variables\n", "\n", "\n", " #### [Back to main page](https://petrosyan.page/fall2020math3215)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Definition (cdf)**\n", "\n", "
\n", "\n", "Let $X$ be any random variable (does not have to be discrete). Define the cdf of $X$ as before\n", "\n", "$$F(x)=P(X\\leq x).$$\n", "\n", "
\n", " \n", " \n", "**Definition (Continuous random variable)**\n", "\n", "
\n", " \n", "A function $F:\\mathbb{R}\\to [0,1]$ is a cdf of some random variable, if and only if\n", "\n", "1. $F$ is non-decreasing:\n", "$x\\leq y\\Rightarrow F(x)\\leq F(y)$\n", "\n", "2. $\\lim\\limits_{x\\to -\\infty}F(x)=0$\n", "\n", "3. $\\lim\\limits_{x\\to \\infty}F(x)=1$\n", "\n", "4. $F$ is right continuous: for any $x\\in \\mathbb{R}$, $\\lim\\limits_{y\\to x^+}f(y)=f(x).$\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An example of a pdf is given by \n", "\n", "$$f(x)=\\frac{1}{\\pi}\\frac{\\sin^2x}{ x^2}, \\quad x\\in\\mathbb{R}.$$\n", "\n", "This is indeed a pdf, because it is non-negative and, as it can be checked, \n", "\n", "$$\\int\\limits_\\mathbb{R}\\frac{\\sin^2x}{ x^2}=\\pi.$$\n", "\n", "Below we plot the pdf of this distribution.\n", "\n" ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "cb1c946c5c23406795094f4c73cfe95d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.6, description='x', max=10.0, min=-10.0, readout_format=''), Output(…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "\n", "x=0.5\n", "def cdf_pdf(x):\n", " xdata = np.delete(np.linspace(-10, 10, 1000), [0])\n", " def pdf_func(x):\n", " y = np.divide(np.sin(x)**2,x**2)/np.pi\n", " return y\n", "\n", "\n", " plt.plot(xdata, pdf_func(xdata))\n", " xshade = xdata[xdata<=x]\n", " plt.fill_between(xshade, pdf_func(xshade), alpha=0.3)\n", " plt.scatter(x,0, s=30)\n", " plt.rcParams['figure.figsize'] = (8, 4)\n", " plt.axhline(y=0, color='k', linewidth=0.5)\n", " plt.xlim(-11,11)\n", " plt.ylim(0, 0.4)\n", " plt.gca().spines['top'].set_visible(False)\n", " plt.gca().spines['right'].set_visible(False)\n", " plt.xticks([x],[\"x={}\".format(x)])\n", " plt.figtext(0.6,0.6, r\"$f(x)=\\frac{\\sin^2x}{ \\pi x^2}$\", ha=\"left\", va=\"top\",\n", " backgroundcolor=(0, 0, 0, 0), fontsize=\"large\")\n", " plt.show();\n", "\n", "# create interactive variables\n", "x = FloatSlider(min=-10.0, max=10.0, step=0.1, value=0.6, readout_format='')\n", "\n", "# display the interactive plot\n", "interact(cdf_pdf, x=x);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Logistic function\n", "\n", "$$F(X)=\\frac{e^x}{1+e^x}\\quad \\Rightarrow \\quad f(x)=\\frac{e^x}{(1+e^x)^2}.$$\n" ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "14fac87e097c4f568cf80fbe8a484dfe", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.6, description='x', max=10.0, min=-10.0, readout_format=''), Output(…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (16, 5)\n", "\n", "\n", "def logistic_cdf_pdf(x):\n", " xdata = np.linspace(-10, 10, 1000)\n", " def cdf_func(xdata):\n", " val = np.divide(np.exp(xdata), 1+np.exp(xdata))\n", " return val\n", " def pdf_func(xdata):\n", " val = np.divide(np.exp(xdata), (1+np.exp(xdata)**2))\n", " return val\n", " \n", " fig, [ax1, ax2] = plt.subplots(1, 2)\n", " \n", " ax1.plot(xdata, pdf_func(xdata))\n", " xshade = xdata[xdata<=x]\n", " ax1.fill_between(xshade, pdf_func(xshade), alpha=0.3)\n", " ax1.scatter(x,0, s=30)\n", " ax1.set_xlim(-10, 10)\n", " ax1.set_ylim(0, 0.6) \n", " ax1.spines[\"top\"].set_visible(False) \n", " ax1.spines[\"right\"].set_visible(False) \n", " ax1.set_xticks([x])\n", " ax1.set_xticklabels([\"x={}\".format(x)])\n", " ax1.set_title(\"pdf\")\n", " \n", " ax2.plot(xdata, cdf_func(xdata))\n", " ax2.vlines(x, 0, cdf_func(x), linestyle=\"dashed\", alpha=0.4)\n", " ax2.scatter(x,0, s=30)\n", " ax2.set_xlim(-10, 10)\n", " ax2.set_ylim(0, 1) \n", " ax2.spines[\"top\"].set_visible(False) \n", " ax2.spines[\"right\"].set_visible(False) \n", " ax2.set_xticks([x])\n", " ax2.set_xticklabels([\"x={}\".format(x)])\n", " ax2.set_title(\"cdf\")\n", " \n", " plt.show();\n", " \n", "# create interactive variables\n", "x = FloatSlider(min=-10, max=10, step=0.1, value=0.6, readout_format='')\n", "\n", "# display the interactive plot\n", "interact(logistic_cdf_pdf, x=x); \n", " \n", " \n" ] }, { "cell_type": "code", "execution_count": 166, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "dcd17b3b7d6a4059ae05b9a7223e79a9", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.6, description='x', max=1.0, readout_format=''), IntSlider(value=0, …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (16, 5)\n", "\n", "a=0\n", "b=1\n", "\n", "def uniform_cdf_pdf(x, a=a, b=b):\n", " xdata = np.linspace(a-1, b+1, 1000)\n", " def cdf_func(xdata):\n", " f0 = lambda y: (y-a)/(b-a)\n", " val = np.piecewise(xdata, [xdata=a) & (xdata<=b), xdata>b], [0, f0, 1])\n", " return val\n", " def pdf_func(y):\n", " val = np.piecewise(y, [y=a) & (y<=b), y>b], [0, 1, 0])\n", " return val\n", " \n", " fig, [ax2, ax1] = plt.subplots(1, 2)\n", " \n", " ax1.plot(xdata, pdf_func(xdata))\n", " xshade = xdata[xdata<=x]\n", " ax1.fill_between(xshade, pdf_func(xshade), alpha=0.3)\n", " ax1.scatter(x,0, s=30)\n", " ax1.set_xlim(a-1, b+1)\n", " ax1.set_ylim(0, 1) \n", " ax1.spines[\"top\"].set_visible(False) \n", " ax1.spines[\"right\"].set_visible(False) \n", " ax1.set_xticks([a, x, b])\n", " ax1.set_xticklabels([\"a={}\".format(a), \"x={}\".format(x), \"b={}\".format(b)])\n", " ax1.set_title(\"pdf\")\n", " \n", " ax2.plot(xdata, cdf_func(xdata))\n", " ax2.vlines(x, 0, cdf_func(x), linestyle=\"dashed\", alpha=0.4)\n", " ax2.scatter(x,0, s=30)\n", " ax2.set_xlim(a-1, b+1)\n", " ax2.set_ylim(0, 1) \n", " ax2.spines[\"top\"].set_visible(False) \n", " ax2.spines[\"right\"].set_visible(False) \n", " ax2.set_xticks([a, x, b])\n", " ax2.set_xticklabels([\"a={}\".format(a), \"x={}\".format(x), \"b={}\".format(b)])\n", " ax2.set_title(\"cdf\")\n", " \n", " plt.show();\n", " \n", "# create interactive variables\n", "x = FloatSlider(min=-a, max=b, step=0.1, value=0.6, readout_format='')\n", "\n", "# display the interactive plot\n", "interact(uniform_cdf_pdf, x=x); \n", " \n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean of the uniform distribution is \n", "\n", "$$\\mu=\\frac{a+b}{2}.$$" ] }, { "cell_type": "code", "execution_count": 167, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "lmbd = 0.8\n", "x=1\n", "\n", "xdata = np.linspace(-1, 10, 1000)\n", "def pdf_func(xdata):\n", " f1 = lambda y: np.exp(-lmbd *(y + np.abs(y))/2)\n", " val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n", " return val\n", "\n", "\n", "plt.plot(xdata, pdf_func(xdata))\n", "xshade = xdata[xdata<=x]\n", "plt.fill_between(xshade, pdf_func(xshade), alpha=0.2)\n", "plt.xticks([x],[\"x={}\".format(x)])\n", "plt.ylim(0, 1)\n", "plt.gca().spines['top'].set_visible(False)\n", "plt.gca().spines['right'].set_visible(False)\n", "plt.figtext(0.5,0.5, r\" $\\lambda=${}\".format(lmbd), ha=\"left\", va=\"top\",\n", " backgroundcolor=(0.1, 0.1, 1, 0.15), fontsize=\"large\")\n", "plt.title(\"pdf of exponential distribution\")\n", "\n", "plt.show();\n", " \n" ] }, { "cell_type": "code", "execution_count": 148, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.special import gamma \n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "\n", "Alpha = [1, 1.5, 2, 3]\n", "Theta = [3.5, 3.5, 3.5, 3.5 ]\n", "\n", "def pdf_func(xdata, alpha, theta):\n", " f1 = lambda y: np.power(y, alpha-1)*np.exp(-y/2)/(np.power(theta,alpha)*gamma(alpha))\n", " val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n", " return val\n", "\n", "fix, ax = plt.subplots()\n", "\n", "def pplot_gamma(theta, alpha, ax):\n", " xdata = np.linspace(-1, 20, 1000)\n", " ax.plot(xdata, pdf_func(xdata, alpha, theta), label=r\"$\\theta=${}, $\\alpha=${}\".format(theta, alpha))\n", " ax.axhline(y=0, color='k', linewidth=0.5)\n", " ax.set_ylim(0, 0.4) \n", " ax.spines[\"top\"].set_visible(False) \n", " ax.spines[\"right\"].set_visible(False)\n", "\n", "for t,a in zip(Theta, Alpha):\n", " pplot_gamma(t, a, ax)\n", " \n", "ax.set_title(\"pdf of Gamma distribution\")\n", "plt.legend() \n", "plt.show();\n" ] }, { "cell_type": "code", "execution_count": 151, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.special import gamma \n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "\n", "r_values = [2, 3, 4, 5, 10]\n", "\n", "def pdf_func(xdata, alpha, theta):\n", " f1 = lambda y: np.power(y, alpha-1)*np.exp(-y/2)/(np.power(theta,alpha)*gamma(alpha))\n", " val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n", " return val\n", "\n", "fix, ax = plt.subplots()\n", "\n", "def pplot_chi(r):\n", " alpha = r/2\n", " xdata = np.linspace(-1, 30, 1000)\n", " ax.plot(xdata, pdf_func(xdata, alpha, theta=2), label=\"r={}\".format(r))\n", " ax.set_ylim(0, 0.5) \n", " ax.spines[\"top\"].set_visible(False) \n", " ax.spines[\"right\"].set_visible(False)\n", "\n", "for r in r_values:\n", " pplot_chi(r)\n", " \n", "ax.set_title(r\"pdf of $\\chi^2$ distribution\")\n", "plt.legend() \n", "plt.show();" ] }, { "cell_type": "code", "execution_count": 152, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.special import gamma \n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "\n", "Mu = [0, -15, 10]\n", "Sigma = [1, 7, 5 ]\n", "\n", "def pdf_func(xdata, mu, sigma):\n", " val = np.exp(-np.power(xdata-mu,2)/(2*sigma**2))/(sigma *np.sqrt(2*np.pi))\n", " return val\n", "\n", "fix, ax = plt.subplots()\n", "\n", "def pplot_gamma(mu, sigma, ax):\n", " xdata = np.linspace(-40, 40, 1000)\n", " ax.plot(xdata, pdf_func(xdata, mu, sigma), label=r\"$\\mu=${}, $\\sigma=${}\".format(mu, sigma))\n", " ax.set_ylim(0, 0.5) \n", " ax.spines[\"top\"].set_visible(False) \n", " ax.spines[\"right\"].set_visible(False)\n", "\n", "for mu,sigma in zip(Mu, Sigma):\n", " pplot_gamma(mu, sigma, ax)\n", " \n", "ax.set_title(\"pdf of normal distribution\")\n", "plt.xticks(Mu)\n", "plt.legend() \n", "plt.show();\n" ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.special import gamma \n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "\n", "mu=0\n", "sigma =1\n", "alpha = 0.05\n", "z = 1.645\n", "\n", "def pdf_func(xdata, mu, sigma):\n", " val = np.exp(-np.power(xdata-mu,2)/(2*sigma**2))/(sigma *np.sqrt(2*np.pi))\n", " return val\n", "\n", "fix, ax = plt.subplots()\n", "\n", "def pplot_gamma(mu, sigma, ax, z):\n", " xdata = np.linspace(-5, 5, 1000)\n", " xshade = xdata[xdata-mu/sigma>=-z]\n", " ax.fill_between(xshade, pdf_func(xshade, mu, sigma), alpha=0.3 )\n", " #xshade = xdata[xdata-mu/sigma<=-z]\n", " #ax.fill_between(xshade, pdf_func(xshade, mu, sigma), alpha=0.3, color=\"blue\")\n", " ax.plot(xdata, pdf_func(xdata, mu, sigma), label=r\"$\\mu=${}, $\\sigma=${}\".format(mu, sigma))\n", " ax.set_ylim(0, 0.5) \n", " ax.spines[\"top\"].set_visible(False) \n", " ax.spines[\"right\"].set_visible(False)\n", " \n", "pplot_gamma(mu, sigma, ax, z)\n", " \n", "ax.set_title(\"pdf of standard normal distribution\")\n", "plt.xticks([-4,0,4])\n", "plt.legend() \n", "plt.show();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mixture distribution" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "lmbd = 0.8\n", "x=1\n", "\n", "xdata = np.linspace(-5, 5, 1001)\n", "def cdf_func1(xdata):\n", " f = lambda y: np.exp(y)/(1+np.exp(y))\n", " return f(xdata)\n", "\n", "def cdf_func2(xdata):\n", " val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, 1])\n", " return val\n", "\n", "plt.plot(xdata, cdf_func1(xdata), linewidth=3)\n", "xshade = xdata[xdata<=x]\n", "plt.ylim(0, 1)\n", "plt.gca().spines['top'].set_visible(False)\n", "plt.gca().spines['right'].set_visible(False)\n", "plt.title(\"cdf of continuous\")\n", "plt.show();" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "lmbd = 0.8\n", "x=1\n", "\n", "xdata = np.linspace(-5, 5, 1001)\n", "def cdf_func1(xdata):\n", " f = lambda y: np.exp(y)/(1+np.exp(y))\n", " return f(xdata)\n", "\n", "def cdf_func2(xdata):\n", " val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, 1])\n", " return val\n", "\n", "plt.plot(xdata, cdf_func2(xdata), linewidth=3)\n", "xshade = xdata[xdata<=x]\n", "plt.ylim(0, 1)\n", "plt.gca().spines['top'].set_visible(False)\n", "plt.gca().spines['right'].set_visible(False)\n", "plt.title(\"cdf of discrete\")\n", "plt.show();" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ipywidgets import interact, FloatSlider\n", "plt.rcParams['figure.figsize'] = (12, 8)\n", "import matplotlib as mpl\n", "mpl.rcParams.update(mpl.rcParamsDefault)\n", "lmbd = 0.8\n", "x=1\n", "\n", "xdata = np.linspace(-5, 5, 1001)\n", "def cdf_func1(xdata):\n", " f = lambda y: np.exp(y)/(1+np.exp(y))\n", " return f(xdata)\n", "\n", "def cdf_func2(xdata):\n", " val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, 1])\n", " return val\n", "\n", "plt.plot(xdata, cdf_func1(xdata)/2+cdf_func2(xdata)/2, linewidth=3)\n", "xshade = xdata[xdata<=x]\n", "plt.ylim(0, 1)\n", "plt.gca().spines['top'].set_visible(False)\n", "plt.gca().spines['right'].set_visible(False)\n", "plt.title(\"cdf of mixture\")\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Density histogram" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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qWbt2bYuaZWZm1tlaEdS3ALtHxL7AfwGX59NVo27UW0hELIiI7ojoHj9+fAuaZWZm1vkGHdQR8VREbMzvLwNGSxpH1oOeVKi6G7B6sOszMzMbSQYd1JImSFJ+/4B8meuA5cBUSXtIGgPMBpYOdn1mZmYjyahGFSRdBMwAxknqBU4DRgNExHzgKODjkjYBzwGzIyKATZLmAlcDXcDCiLhzSLbCzMysopRlalq6u7ujp6en3c0wMzMbLrXO6wJ8ZTIzM7OkOajNzMwS5qA2MzNLmIPazMwsYQ5qMzOzhDmozczMEuagNjMzS5iD2szMLGEOajMzs4Q5qM3MzBLmoDYzM0uYg9rMzCxhDmozM7OEOajNzMwS5qA2MzNLmIPazMwsYQ5qMzOzhDmozczMEtYwqCUtlLRG0oo65cdIuj2/3SBp30LZKkl3SLpVUk8rG25mZjYSlOlRLwJmbqb8T8D0iNgH+DKwoF/5wRGxX0R0N9dEMzOzkWtUowoRcZ2kKZspv6Hw8CZgt8E3y8zMzKD131EfB1xZeBzANZJuljRnczNKmiOpR1LP2rVrW9wsMzOzztSwR12WpIPJgvpthckHRcRqSTsB10q6JyKuqzV/RCwgHzbv7u6OVrXLzMysk7WkRy1pH+A8YFZErOubHhGr879rgCXAAa1Yn5mZ2Ugx6KCWNBm4DDg2Iu4rTN9K0ti++8AhQM0zx83MzKy2hkPfki4CZgDjJPUCpwGjASJiPnAqsCNwriSATfkZ3jsDS/Jpo4ALI+KqIdgGMzOzylJEel8Hd3d3R0+Pf3ZtZmYjhuoV+MpkZlZpEybtjqTK3SZM2r3dT60Nk5ad9W1mlqLHeh+k6wcPt7sZLffYxya2uwk2TNyjNjMzS5iD2szMLGEOajMzs4Q5qM3MzBLmoDYzM0uYg9rMzCxhDmozM7OEOajNzMwS5qA2MzNLmIPazMwsYQ5qsyb4+tFmNlx8rW+zJvj60WY2XNyjNjMzS5iD2szMLGEOajMzs4Q5qM3MzBLWMKglLZS0RtKKOuWSdLaklZJul7R/oWympHvzsnmtbLiZmdlIUKZHvQiYuZnyQ4Gp+W0O8D0ASV3AOXn5XsDRkvYaTGPNzMxGmoY/z4qI6yRN2UyVWcDiiAjgJknbSdoFmAKsjIj7ASRdnNe9a7CNtgQ88QQcfDD09ra7JW2xFuAzb2x3M4bGuHHtbkFLjdjXSoKTToJ5HszsdK34HfVE4KHC4958Wq3p0+otRNIcsh45kydPbkGzbEj19MBtt7W7FW0zDmDjE+1uxtBYt67dLWipEf1aXXSRg7oCWhHUqjEtNjO9pohYACwA6O7urlvPEhH5SzR9OlxySXvb0gbjxo+n69t3tLsZLffSZ/fm8bVr292MlhqRr9WKFdmIV/ijtApaEdS9wKTC492A1cCYOtOtSsaMaThUOmHS7jzW++AwNWj4dI3dod1NaLmXRr0GjR/f7ma0XCVfK6i/722//XA2xYZYK4J6KTA3/w56GrAhIh6RtBaYKmkP4GFgNvDBFqzPUtB3pK5aAyevVMXLbb5U1UttbvqzX6sq6Nsv3aOuhIZBLekiYAYwTlIvcBowGiAi5gPLgMOAlcCzwEfzsk2S5gJXA13Awoi4cwi2wdrBHwBm6fN+Wgllzvo+ukF5AP9Sp2wZWZBbVZXoUZvZMPN+WSm+Mpk1ZwBD32Y2zDz0XSkOamuOPwDM0uf9tBIc1DY47lGbpcf7ZaU4qK05Hvo2S5eHvivFQW3N8QeAWfq8n1aCg9oGxz1qs/R4v6wUB7U1x0PfZuny0HelOKitOf4AMEuf99NKcFDb4LhHbZYe75eV4qC25njo2yxdHvquFAe1NccfAGbp835aCQ5qGxz3qM3S4/2yUhzU1hwfqZuly0PfleKgtub4O2qz9DmoK8FBbYPjoDZLj/fLSnFQW3N8pG6WLg99V4qD2prjoW+z9DmoK8FBbYPjoDZLj/fLSikV1JJmSrpX0kpJ82qUf17SrflthaSXJO2Ql62SdEde1tPqDbA28ZG6Wbo89F0poxpVkNQFnAO8C+gFlktaGhF39dWJiG8A38jrHwF8JiLWFxZzcEQ83tKWW3t56NssfQ7qSijToz4AWBkR90fEC8DFwKzN1D8auKgVjbMO4KA2S4/3y0opE9QTgYcKj3vzaa8iaUtgJnBpYXIA10i6WdKceiuRNEdSj6SetWvXlmiWtZWP1M3S5aHvSikT1LUOzeq9+kcA1/cb9j4oIvYHDgX+RdI7as0YEQsiojsiusePH1+iWdZWHvo2S5+DuhLKBHUvMKnweDdgdZ26s+k37B0Rq/O/a4AlZEPpVhUOarP0eL+slDJBvRyYKmkPSWPIwnhp/0qStgWmAz8rTNtK0ti++8AhwIpWNNzazEfqZuny0HelNDzrOyI2SZoLXA10AQsj4k5JJ+bl8/Oq7wWuiYhnCrPvDCxR9qYZBVwYEVe1cgOsTTz0bZY+B3UlNAxqgIhYBizrN21+v8eLgEX9pt0P7DuoFlraHNRm6fF+WSm+Mpk1x0fqZuny0HelOKitOR76Nkufg7oSHNQ2OA5qs/R4v6wUB7U1x0fqZuny0HelOKhtcHzkbmY2pBzU1hwfqZulyz3qSnFQW3N8MplZ+hzUleCgtsFxUJulx/tlpTiorTk+UjdLl4e+K8VBbc3x0LdZ+hzUleCgtsFxUJulx/tlpTiorTk+UjdLl4e+K8VBbc3x0LdZ+hzUleCgtsFxUJulx/tlpTiorTk+UjdLl4e+K8VBbc3x0LdZ+hzUleCgtsFxUJulx/tlpTiorTk+UjdLl4e+K6VUUEuaKeleSSslzatRPkPSBkm35rdTy85rHcpD32bpc1BXwqhGFSR1AecA7wJ6geWSlkbEXf2q/iYiDm9yXutUDmqz9Hi/rJQyPeoDgJURcX9EvABcDMwqufzBzGsp85G6Wbo89F0pZYJ6IvBQ4XFvPq2/AyXdJulKSW8Y4LxImiOpR1LP2rVrSzTL2spD32bpc1BXQpmgrvVJ3P/VvwXYPSL2Bf4LuHwA82YTIxZERHdEdI8fP75EsywJDmqz9Hi/rJQyQd0LTCo83g1YXawQEU9FxMb8/jJgtKRxZea1DuUjdbN0eei7UsoE9XJgqqQ9JI0BZgNLixUkTZCyd4akA/Llriszr3UoD32bpc9BXQkNz/qOiE2S5gJXA13Awoi4U9KJefl84Cjg45I2Ac8BsyMigJrzDtG2mJkZ+AC6YhoGNbw8nL2s37T5hfvfBb5bdl6rAPeozdLloe9K8ZXJrDkOarP0OagrwUFtZlY1PoCuFAe1Ncc9arN0eei7UhzU1hwHtVn6HNSV4KA2M6saH0BXioPamuMetVm6PPRdKQ5qa46D2ix9DupKcFCbmVWND6ArxUFtzXGP2ixdHvquFAe1NcdBbZY+B3UlOKjNzKrGB9CV4qC25rhHbZYu75eV4qC25jiozTqDh787noPazKxqfABdKQ5qa4571GadwT3qjuegtuY4qM06g4O64zmozcyqyAfRleGgtua4R22WNl/0pDJKBbWkmZLulbRS0rwa5cdIuj2/3SBp30LZKkl3SLpVUk8rG29t5J3frDN4X+14oxpVkNQFnAO8C+gFlktaGhF3Far9CZgeEU9IOhRYAEwrlB8cEY+3sN2WCveozdLkfbMyyvSoDwBWRsT9EfECcDEwq1ghIm6IiCfyhzcBu7W2mZYcD32bpc1D35VRJqgnAg8VHvfm0+o5Driy8DiAayTdLGnOwJtoZmY2cjUc+gZqdZlqHqJJOpgsqN9WmHxQRKyWtBNwraR7IuK6GvPOAeYATJ48uUSzrK3cozZLm3vUlVGmR90LTCo83g1Y3b+SpH2A84BZEbGub3pErM7/rgGWkA2lv0pELIiI7ojoHj9+fPktsPZwUJt1Bgd1xysT1MuBqZL2kDQGmA0sLVaQNBm4DDg2Iu4rTN9K0ti++8AhwIpWNd7MzOrwQXRlNBz6johNkuYCVwNdwMKIuFPSiXn5fOBUYEfgXGVvjk0R0Q3sDCzJp40CLoyIq4ZkS2x4uUdtljYPfVdGme+oiYhlwLJ+0+YX7h8PHF9jvvuBfftPtwpwUJt1Bgd1x/OVyczMqsgH0ZXhoLbmuEdtljYPfVeGg9qa46A26wwO6o7noDYzqyIfRFeGg9qa4x61Wdo89F0ZDmprjoParDM4qDueg9rMrIp8EF0ZDmprjnvUZmnz0HdlOKitOQ5qs87goO54DmozsyryQXRlOKitOe5Rm6XNQ9+V4aC25njnN+sM3lc7noPaBsc9arM0ed+sDAe1NcdD32Zp89B3ZTiorTne+c06g/fVjuegtsFxj9osTd43K8NBbc3x0LdZ2jz0XRkOamuOd36zzuB9teM5qG1w3KM2S5P3zcooFdSSZkq6V9JKSfNqlEvS2Xn57ZL2LzuvdSgPfZulzUPflTGqUQVJXcA5wLuAXmC5pKURcVeh2qHA1Pw2DfgeMK3kvDZU7rsPnn56aJb96KNDs1wza63bboMddxyaZU+dCttsMzTLtpc1DGrgAGBlRNwPIOliYBZQDNtZwOKICOAmSdtJ2gWYUmJeGypz58K11w7tOrq6hnb5Ztacvn3z3e8eunVcfTUccsjQLd8AUDQYFpF0FDAzIo7PHx8LTIuIuYU6VwBnRsRv88e/BE4mC+rNzltYxhxgTv7w9cC9g9u0thoHPN7uRgyTkbKt3s5q8XZWSxW28/GImFmroEyPutaXkP3TvV6dMvNmEyMWAAtKtCd5knoiorvd7RgOI2VbvZ3V4u2slqpvZ5mg7gUmFR7vBqwuWWdMiXnNzMysjjJnfS8HpkraQ9IYYDawtF+dpcCH8rO/3wJsiIhHSs5rZmZmdTTsUUfEJklzgauBLmBhRNwp6cS8fD6wDDgMWAk8C3x0c/MOyZakpRJD+CWNlG31dlaLt7NaKr2dDU8mMzMzs/bxlcnMzMwS5qA2MzNLmIO6SZJ2kHStpD/kf7evUWeSpF9JulvSnZI+VSg7XdLDkm7Nb4cN7xZs3ki5bGyJ7Twm377bJd0gad9C2SpJd+SvX8/wtnxgSmznDEkbCu/HU8vOm5IS2/n5wjaukPSSpB3ysk56PRdKWiNpRZ3yquyfjbazEvtnQxHhWxM34OvAvPz+POA/atTZBdg/vz8WuA/YK398OvC5dm9HnW3rAv4I/DXZT+xu62t3oc5hwJVkv5V/C/C7svOmciu5nW8Fts/vH9q3nfnjVcC4dm9Hi7ZzBnBFM/OmchtoW4EjgP/ptNczb+s7gP2BFXXKO37/LLmdHb9/lrm5R928WcCP8vs/Ao7sXyEiHomIW/L7TwN3AxOHrYXNe/mysRHxAtB36deily8bGxE3AX2XjS0zbyoatjUiboiIJ/KHN5FdC6DTDOY1qdTr2c/RwEXD0rIWi4jrgPWbqVKF/bPhdlZk/2zIQd28nSP7rTj53502V1nSFOBNwO8Kk+fmQzYLaw2dt9FE4KHC415efYBRr06ZeVMx0LYeR9ZL6RPANZJuzi+Bm6qy23mgpNskXSnpDQOcNwWl2yppS2AmcGlhcqe8nmVUYf8cqE7dPxsqc2WyEUvSL4AJNYq+OMDlbE32gfDpiHgqn/w94Mtkb6YvA98C/rn51rbUsFw2NgGl2yrpYLIPgrcVJh8UEasl7QRcK+mevAeQmjLbeQuwe0RszM+XuJzsv+FV8vUkG/a+PiKKvbVOeT3LqML+WVqH758NOag3IyLeWa9M0mOSdomIR/IhpTV16o0mC+kLIuKywrIfK9T5AXBF61o+aCPlsrFlthNJ+wDnAYdGxLq+6RGxOv+7RtISsmHFFD8IGm5n4QCSiFgm6VxJ48rMm5CBtHU2/Ya9O+j1LKMK+2cpFdg/G/LQd/OWAh/O738Y+Fn/CpIE/BC4OyK+3a9sl8LD9wI1z2psk5Fy2diGbZU0GbgMODYi7itM30rS2L77wCGk9RoWldnOCfn7FUkHkH02rCszb0JKtVXStsB0Cvtsh72eZVRh/2yoIvtnQ+5RN+9M4L8lHQc8CPwfAEm7AudFxGHAQcCxwB2Sbs3nOyUilgFfl7Qf2bDTKuCEYW5/XaaSV/QAAACUSURBVDFCLhtbcjtPBXYEzs1zbFNk/6VnZ2BJPm0UcGFEXNWGzWio5HYeBXxc0ibgOWB2RARQtdcTsgPjayLimcLsHfN6Aki6iOxM/XGSeoHTgNFQnf0TSm1nx++fZfgSomZmZgnz0LeZmVnCHNRmZmYJc1CbmZklzEFtZmaWMAe1mZlZwhzUZmZmCXNQm5mZJez/A81FQzcl3OPAAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# nbi:hide_in\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.rcParams[\"figure.figsize\"] = (8, 4)\n", "\n", "n=40 #max number of samples\n", "a=0\n", "b=1\n", "\n", "data =np.round(np.random.rand(n)*(b-a)+a, 2)\n", "\n", "def pdf_func(xdata, a, b):\n", " val = 1/(b-a)\n", " val = np.piecewise(xdata, \n", " [xdataa) & (xdatab], \n", " [0, np.nan, val, np.nan, 0])\n", " return val\n", "\n", "def epmf(data, inter, N):\n", " epmf_values = np.zeros(N)\n", " for i in range(N): \n", " length = inter[i+1]-inter[i]\n", " epmf_values[i] = np.sum((inter[i]<=data) & (data