{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Create a truncated distribution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this example we are going to define truncated distributions.\n",
"\n",
"It is possible to truncate a distribution in its lower area, or its upper area or in both lower and upper areas.\n",
"\n",
"In 1-d, assuming a and b bounds, its probability density function is defined as:\n",
"\n",
"$$\\forall y \\in \\mathbb{R}, p_Y(y) =\n",
" \\begin{array}{|ll}\n",
" 0 & \\mbox{for } y \\geq b \\mbox{ or } y \\leq a\\\\\n",
" \\displaystyle \\frac{1}{F_X(b) - F_X(a)}\\, p_X(y) & \\mbox{for } y\\in[a,b]\n",
" \\end{array}$$\n",
"\n",
"Is is also possible to truncate a multivariate distribution."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
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"\n"
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]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from __future__ import print_function\n",
"import openturns as ot\n",
"\n",
"# the original distribution\n",
"distribution = ot.Gumbel(0.45, 0.6)\n",
"distribution.drawPDF()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
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]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# truncate on the left\n",
"truncated = ot.TruncatedDistribution(distribution, 0.2, ot.TruncatedDistribution.LOWER)\n",
"truncated.drawPDF()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
],
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]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# truncate on the right\n",
"truncated = ot.TruncatedDistribution(distribution, 1.5, ot.TruncatedDistribution.UPPER)\n",
"truncated.drawPDF()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
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],
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]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# truncated on both bounds\n",
"truncated = ot.TruncatedDistribution(distribution, 0.2, 1.5)\n",
"truncated.drawPDF()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Define a multivariate distribution\n",
"dimension = 2\n",
"size = 70\n",
"sample = ot.Normal(dimension).getSample(size)\n",
"ks = ot.KernelSmoothing().build(sample)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Truncate it between (-2;2)^n\n",
"bounds = ot.Interval([-2.0] * dimension, [2.0] * dimension)\n",
"truncatedKS = ot.Distribution(ot.TruncatedDistribution(ks, bounds))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
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]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Draw its PDF\n",
"graph = truncatedKS.drawPDF([-2.5] * dimension, [2.5] * dimension, [256] * dimension)\n",
"graph.add(ot.Cloud(truncatedKS.getSample(200)))\n",
"graph.setColors([\"blue\", \"red\"])\n",
"graph"
]
}
],
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