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docs: improve README examples of
stats/base/dists/chi
namespace
PR-URL: #1803 Ref: #1618 Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com> Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com>
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@@ -101,15 +101,91 @@ var mu = dist.mean; | |
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## Examples | ||
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<!-- TODO: better examples --> | ||
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<!-- eslint no-undef: "error" --> | ||
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```javascript | ||
var objectKeys = require( '@stdlib/utils/keys' ); | ||
var chiRandomFactory = require( '@stdlib/random/base/chi' ).factory; | ||
var filledarrayBy = require( '@stdlib/array/filled-by' ); | ||
var variance = require( '@stdlib/stats/base/variance' ); | ||
var linspace = require( '@stdlib/array/base/linspace' ); | ||
var rayleigh = require( '@stdlib/stats/base/dists/rayleigh' ); | ||
var mean = require( '@stdlib/stats/base/mean' ); | ||
var abs = require( '@stdlib/math/base/special/abs' ); | ||
var chi = require( '@stdlib/stats/base/dists/chi' ); | ||
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console.log( objectKeys( chi ) ); | ||
// Define the degrees of freedom parameter: | ||
var k = 2; | ||
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// Generate an array of x values: | ||
var x = linspace( 0, 10, 100 ); | ||
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// Compute the PDF for each x: | ||
var chiPDF = chi.pdf.factory( k ); | ||
var pdf = filledarrayBy( x.length, 'float64', chiPDF ); | ||
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// Compute the CDF for each x: | ||
var chiCDF = chi.cdf.factory( k ); | ||
var cdf = filledarrayBy( x.length, 'float64', chiCDF ); | ||
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// Output the PDF and CDF values: | ||
console.log( 'x values:', x ); | ||
console.log( 'PDF values:', pdf ); | ||
console.log( 'CDF values:', cdf ); | ||
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// Compute statistical properties: | ||
var theoreticalMean = chi.mean( k ); | ||
var theoreticalVariance = chi.variance( k ); | ||
var theoreticalSkewness = chi.skewness( k ); | ||
var theoreticalKurtosis = chi.kurtosis( k ); | ||
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console.log( 'Theoretical Mean:', theoreticalMean ); | ||
console.log( 'Theoretical Variance:', theoreticalVariance ); | ||
console.log( 'Skewness:', theoreticalSkewness ); | ||
console.log( 'Kurtosis:', theoreticalKurtosis ); | ||
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// Generate random samples from the Chi distribution: | ||
var rchi = chiRandomFactory( k ); | ||
var n = 1000; | ||
var samples = filledarrayBy( n, 'float64', rchi ); | ||
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// Compute sample mean and variance: | ||
var sampleMean = mean( n, samples, 1 ); | ||
var sampleVariance = variance( n, 1, samples, 1 ); | ||
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console.log( 'Sample Mean:', sampleMean ); | ||
console.log( 'Sample Variance:', sampleVariance ); | ||
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// Compare sample statistics to theoretical values: | ||
console.log( 'Difference in Mean:', abs( theoreticalMean - sampleMean ) ); | ||
console.log( 'Difference in Variance:', abs( theoreticalVariance - sampleVariance ) ); | ||
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// Demonstrate the relationship with the Rayleigh distribution when k=2: | ||
var rayleighPDF = rayleigh.pdf.factory( 1.0 ); | ||
var rayleighCDF = rayleigh.cdf.factory( 1.0 ); | ||
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// Compute Rayleigh PDF and CDF for each x: | ||
var rayleighPDFValues = filledarrayBy( x.length, 'float64', rayleighPDF ); | ||
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var rayleighCDFValues = filledarrayBy( x.length, 'float64', rayleighCDF ); | ||
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// Compare Chi and Rayleigh PDFs and CDFs: | ||
var maxDiffPDF = 0.0; | ||
var maxDiffCDF = 0.0; | ||
var diffPDF; | ||
var diffCDF; | ||
var i; | ||
for ( i = 0; i < x.length; i++ ) { | ||
diffPDF = abs( pdf[ i ] - rayleighPDFValues[ i ] ); | ||
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kgryte
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if ( diffPDF > maxDiffPDF ) { | ||
maxDiffPDF = diffPDF; | ||
} | ||
diffCDF = abs( cdf[ i ] - rayleighCDFValues[ i ] ); | ||
if ( diffCDF > maxDiffCDF ) { | ||
maxDiffCDF = diffCDF; | ||
} | ||
} | ||
console.log( 'Maximum difference between Chi(k=2) PDF and Rayleigh PDF:', maxDiffPDF ); | ||
console.log( 'Maximum difference between Chi(k=2) CDF and Rayleigh CDF:', maxDiffCDF ); | ||
``` | ||
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</section> | ||
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Coverage Report
Package | Statements | Branches | Functions | Lines |
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stats/base/dists/chi |
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The above coverage report was generated for the changes in this push.
@Planeshifter This can be simplified slightly using https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/utils/absolute-difference.