{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Create univariate and multivariate distributions: a quick start guide to distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Abstract \n", "\n", "In this example, we present classes for univariate and multivariate distributions. We demonstrate the probabilistic programming capabilities of the library. For univariate distributions, we show how to compute the probability density, the cumulated probability density and the quantiles. We also show how to create graphics. The `ComposedDistribution` class, which creates a distribution based on its marginals and its copula, is presented. We show how to truncate any distribution with the `TruncatedDistribution` class." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Univariate distribution\n", "\n", "The library is a probabilistic programming library: it is possible to create a random variable and perform operations on this variable *without* generating a sample. \n", "\n", "In the OpenTURNS platform, several *univariate distributions* are implemented. The most commonly used are:\n", "\n", " - `Uniform`,\n", " - `Normal`,\n", " - `Beta`, \n", " - `LogNormal`, \n", " - `Exponential`, \n", " - `Weibull`." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import openturns as ot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The uniform distribution\n", "\n", "Let us create a uniform random variable $\\mathcal{U}(2,5)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "uniform = ot.Uniform(2,5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `drawPDF` method plots the probability density function." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "class=Graph name=pdf as a function of X0 implementation=class=GraphImplementation name=pdf as a function of X0 title= xTitle=X0 yTitle=PDF axes=ON grid=ON legendposition=topright legendFontSize=1 drawables=[class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=X0 PDF data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=129 dimension=2 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color=red fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uniform.drawPDF()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `computePDF` method computes the probability distribution at a specific point." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.3333333333333333" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uniform.computePDF(3.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `drawCDF` method plots the cumulated distribution function." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "class=Graph name=cdf as a function of X0 implementation=class=GraphImplementation name=cdf as a function of X0 title= xTitle=X0 yTitle=CDF axes=ON grid=ON legendposition=topleft legendFontSize=1 drawables=[class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=X0 CDF data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=129 dimension=2 data=[[-0.28,0],[-0.220937,0],[-0.161875,0],[-0.102812,0],[-0.04375,0],[0.0153125,0],[0.074375,0],[0.133438,0],[0.1925,0],[0.251563,0],[0.310625,0],[0.369688,0],[0.42875,0],[0.487813,0],[0.546875,0],[0.605938,0],[0.665,0],[0.724063,0],[0.783125,0],[0.842188,0],[0.90125,0],[0.960313,0],[1.01938,0],[1.07844,0],[1.1375,0],[1.19656,0],[1.25563,0],[1.31469,0],[1.37375,0],[1.43281,0],[1.49188,0],[1.55094,0],[1.61,0],[1.66906,0],[1.72813,0],[1.78719,0],[1.84625,0],[1.90531,0],[1.96438,0],[2.02344,0.0078125],[2.0825,0.0275],[2.14156,0.0471875],[2.20063,0.066875],[2.25969,0.0865625],[2.31875,0.10625],[2.37781,0.125938],[2.43688,0.145625],[2.49594,0.165313],[2.555,0.185],[2.61406,0.204688],[2.67313,0.224375],[2.73219,0.244063],[2.79125,0.26375],[2.85031,0.283438],[2.90938,0.303125],[2.96844,0.322813],[3.0275,0.3425],[3.08656,0.362187],[3.14562,0.381875],[3.20469,0.401562],[3.26375,0.42125],[3.32281,0.440937],[3.38187,0.460625],[3.44094,0.480312],[3.5,0.5],[3.55906,0.519687],[3.61813,0.539375],[3.67719,0.559063],[3.73625,0.57875],[3.79531,0.598437],[3.85438,0.618125],[3.91344,0.637812],[3.9725,0.6575],[4.03156,0.677187],[4.09063,0.696875],[4.14969,0.716562],[4.20875,0.73625],[4.26781,0.755937],[4.32688,0.775625],[4.38594,0.795312],[4.445,0.815],[4.50406,0.834687],[4.56312,0.854375],[4.62219,0.874062],[4.68125,0.89375],[4.74031,0.913438],[4.79937,0.933125],[4.85844,0.952812],[4.9175,0.9725],[4.97656,0.992188],[5.03562,1],[5.09469,1],[5.15375,1],[5.21281,1],[5.27187,1],[5.33094,1],[5.39,1],[5.44906,1],[5.50812,1],[5.56719,1],[5.62625,1],[5.68531,1],[5.74437,1],[5.80344,1],[5.8625,1],[5.92156,1],[5.98062,1],[6.03969,1],[6.09875,1],[6.15781,1],[6.21687,1],[6.27594,1],[6.335,1],[6.39406,1],[6.45312,1],[6.51219,1],[6.57125,1],[6.63031,1],[6.68937,1],[6.74844,1],[6.8075,1],[6.86656,1],[6.92562,1],[6.98469,1],[7.04375,1],[7.10281,1],[7.16187,1],[7.22094,1],[7.28,1]] color=red fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uniform.drawCDF()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `computeCDF` method computes the value of the cumulated distribution function a given point." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uniform.computeCDF(3.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `getSample` method generates a sample." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
X0 | |
---|---|
0 | 3.8896296698233312 |
1 | 4.648415671157781 |
2 | 2.4058290524565233 |
3 | 2.097508253613154 |
4 | 3.0411711236405656 |
5 | 4.908269063404967 |
6 | 4.762038780071152 |
7 | 3.509120454348147 |
8 | 2.1896182295391515 |
9 | 2.878270681243195 |
ComposedDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), IndependentCopula(dimension = 2))
" ], "text/plain": [ "class=ComposedDistribution name=ComposedDistribution dimension=2 copula=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal = ot.Normal()\n", "uniform = ot.Uniform()\n", "distribution = ot.ComposedDistribution([normal, uniform])\n", "distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use the `IndependentCopula` class." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "ComposedDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), IndependentCopula(dimension = 2))
" ], "text/plain": [ "class=ComposedDistribution name=ComposedDistribution dimension=2 copula=class=IndependentCopula name=IndependentCopula dimension=2 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal = ot.Normal()\n", "uniform = ot.Uniform()\n", "copula = ot.IndependentCopula(2)\n", "distribution = ot.ComposedDistribution([normal, uniform], copula)\n", "distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that this produces the same result: in the end of this section, we will change the copula and see what happens." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `getSample` method produces a sample from this distribution." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "X0 | X1 | |
---|---|---|
0 | 1.259887968044958 | 0.08302850200114786 |
1 | -2.1513525835586704 | 0.21233747708031991 |
2 | 0.6383845131142492 | -0.31946948335596526 |
3 | 1.1985967013995071 | -0.3335571137988924 |
4 | 0.5760514867363357 | -0.4738648412897719 |
5 | -2.721057543176531 | 0.6944882272474788 |
6 | -0.45663433946040866 | 0.7525542385695916 |
7 | 0.8344516247016848 | -0.19909337979103858 |
8 | 0.18972282501335233 | -0.49021388839792124 |
9 | -1.5598970035006174 | -0.6660326523710496 |
NormalCopula(R = [[ 1 0.6 ]
\n",
" [ 0.6 1 ]])
ComposedDistribution(Normal(mu = 0, sigma = 1), Uniform(a = -1, b = 1), AliMikhailHaqCopula(theta = 0.9))
" ], "text/plain": [ "class=ComposedDistribution name=ComposedDistribution dimension=2 copula=class=AliMikhailHaqCopula name=AliMikhailHaqCopula dimension=2 theta=0.9 marginal[0]=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] marginal[1]=class=Uniform name=Uniform dimension=1 a=-1 b=1" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal = ot.Normal()\n", "uniform = ot.Uniform()\n", "theta = 0.9\n", "copula = ot.AliMikhailHaqCopula(theta)\n", "distribution = ot.ComposedDistribution([normal, uniform], copula)\n", "distribution" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "class=Graph name=X0~N, X1~U, Ali-Mikhail-Haq copula implementation=class=GraphImplementation name=X0~N, X1~U, Ali-Mikhail-Haq copula title=X0~N, X1~U, Ali-Mikhail-Haq copula xTitle=X0 yTitle=X1 axes=ON grid=ON legendposition= legendFontSize=1 drawables=[class=Drawable name=Unnamed implementation=class=Cloud name=Unnamed derived from class=DrawableImplementation name=Unnamed legend= data=class=Sample name=ComposedDistribution implementation=class=SampleImplementation name=ComposedDistribution size=1000 dimension=2 description=[X0,X1] data=[[-0.643902,-0.13766],[-1.27376,-0.203849],[0.283441,-0.788764],...,[0.417786,0.10767],[0.910473,0.401995],[-0.0597296,-0.333784]] color=blue fillStyle=solid lineStyle=solid pointStyle=fsquare lineWidth=1]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample = distribution.getSample(1000)\n", "showAxes = True\n", "graph = ot.Graph(\"X0~N, X1~U, Ali-Mikhail-Haq copula\", \"X0\", \"X1\", showAxes)\n", "cloud = ot.Cloud(sample, \"blue\", \"fsquare\", \"\") # Create the cloud\n", "graph.add(cloud) # Then, add it to the graph\n", "graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the sample is quite different from the previous sample with independent copula." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Draw several distributions in the same plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is sometimes convenient to create a plot presenting the PDF and CDF on the same graphics. This is possible thanks to Matplotlib." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "beta = ot.Beta(5, 7, 9, 10)\n", "pdfbeta = beta.drawPDF()\n", "cdfbeta = beta.drawCDF()\n", "exponential = ot.Exponential(3)\n", "pdfexp = exponential.drawPDF()\n", "cdfexp = exponential.drawCDF()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import openturns.viewer as otv" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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