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docs: improve README examples of stats/base/dists/chi namespace
PR-URL: #1803 Ref: #1618 Co-authored-by: Philipp Burckhardt <[email protected]> Reviewed-by: Philipp Burckhardt <[email protected]>
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‎lib/node_modules/@stdlib/stats/base/dists/chi/README.md‎

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Original file line numberDiff line numberDiff line change
@@ -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
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var objectKeys = require( '@stdlib/utils/keys' );
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var chiRandomFactory = require( '@stdlib/random/base/chi' ).factory;
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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var variance = require( '@stdlib/stats/base/variance' );
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var linspace = require( '@stdlib/array/base/linspace' );
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var rayleigh = require( '@stdlib/stats/base/dists/rayleigh' );
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var mean = require( '@stdlib/stats/base/mean' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var chi = require( '@stdlib/stats/base/dists/chi' );
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console.log( objectKeys( chi ) );
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// Define the degrees of freedom parameter:
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var k = 2;
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// Generate an array of x values:
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var x = linspace( 0, 10, 100 );
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// Compute the PDF for each x:
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var chiPDF = chi.pdf.factory( k );
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var pdf = filledarrayBy( x.length, 'float64', chiPDF );
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// Compute the CDF for each x:
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var chiCDF = chi.cdf.factory( k );
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var cdf = filledarrayBy( x.length, 'float64', chiCDF );
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// Output the PDF and CDF values:
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console.log( 'x values:', x );
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console.log( 'PDF values:', pdf );
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console.log( 'CDF values:', cdf );
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// Compute statistical properties:
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var theoreticalMean = chi.mean( k );
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var theoreticalVariance = chi.variance( k );
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var theoreticalSkewness = chi.skewness( k );
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var theoreticalKurtosis = chi.kurtosis( k );
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console.log( 'Theoretical Mean:', theoreticalMean );
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console.log( 'Theoretical Variance:', theoreticalVariance );
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console.log( 'Skewness:', theoreticalSkewness );
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console.log( 'Kurtosis:', theoreticalKurtosis );
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// Generate random samples from the Chi distribution:
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var rchi = chiRandomFactory( k );
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var n = 1000;
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var samples = filledarrayBy( n, 'float64', rchi );
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// Compute sample mean and variance:
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var sampleMean = mean( n, samples, 1 );
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var sampleVariance = variance( n, 1, samples, 1 );
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console.log( 'Sample Mean:', sampleMean );
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console.log( 'Sample Variance:', sampleVariance );
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// Compare sample statistics to theoretical values:
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console.log( 'Difference in Mean:', abs( theoreticalMean - sampleMean ) );
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console.log( 'Difference in Variance:', abs( theoreticalVariance - sampleVariance ) );
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// Demonstrate the relationship with the Rayleigh distribution when k=2:
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var rayleighPDF = rayleigh.pdf.factory( 1.0 );
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var rayleighCDF = rayleigh.cdf.factory( 1.0 );
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// Compute Rayleigh PDF and CDF for each x:
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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:
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var maxDiffPDF = 0.0;
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var maxDiffCDF = 0.0;
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var diffPDF;
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var diffCDF;
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var i;
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for ( i = 0; i < x.length; i++ ) {
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diffPDF = abs( pdf[ i ] - rayleighPDFValues[ i ] );
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if ( diffPDF > maxDiffPDF ) {
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maxDiffPDF = diffPDF;
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}
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diffCDF = abs( cdf[ i ] - rayleighCDFValues[ i ] );
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if ( diffCDF > maxDiffCDF ) {
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maxDiffCDF = diffCDF;
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}
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}
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console.log( 'Maximum difference between Chi(k=2) PDF and Rayleigh PDF:', maxDiffPDF );
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console.log( 'Maximum difference between Chi(k=2) CDF and Rayleigh CDF:', maxDiffCDF );
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```
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</section>

‎lib/node_modules/@stdlib/stats/base/dists/chi/examples/index.js‎

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Original file line numberDiff line numberDiff line change
@@ -18,7 +18,85 @@
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'use strict';
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var objectKeys = require( '@stdlib/utils/keys' );
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var chiRandomFactory = require( '@stdlib/random/base/chi' ).factory;
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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var variance = require( '@stdlib/stats/base/variance' );
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var linspace = require( '@stdlib/array/base/linspace' );
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var rayleigh = require( '@stdlib/stats/base/dists/rayleigh' );
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var mean = require( '@stdlib/stats/base/mean' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var chi = require( './../lib' );
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console.log( objectKeys( chi ) );
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// Define the degrees of freedom parameter:
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var k = 2;
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// Generate an array of x values:
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var x = linspace( 0, 10, 100 );
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// Compute the PDF for each x:
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var chiPDF = chi.pdf.factory( k );
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var pdf = filledarrayBy( x.length, 'float64', chiPDF );
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// Compute the CDF for each x:
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var chiCDF = chi.cdf.factory( k );
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var cdf = filledarrayBy( x.length, 'float64', chiCDF );
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// Output the PDF and CDF values:
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console.log( 'x values:', x );
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console.log( 'PDF values:', pdf );
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console.log( 'CDF values:', cdf );
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// Compute statistical properties:
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var theoreticalMean = chi.mean( k );
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var theoreticalVariance = chi.variance( k );
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var theoreticalSkewness = chi.skewness( k );
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var theoreticalKurtosis = chi.kurtosis( k );
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console.log( 'Theoretical Mean:', theoreticalMean );
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console.log( 'Theoretical Variance:', theoreticalVariance );
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console.log( 'Skewness:', theoreticalSkewness );
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console.log( 'Kurtosis:', theoreticalKurtosis );
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// Generate random samples from the Chi distribution:
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var rchi = chiRandomFactory( k );
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var n = 1000;
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var samples = filledarrayBy( n, 'float64', rchi );
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// Compute sample mean and variance:
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var sampleMean = mean( n, samples, 1 );
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var sampleVariance = variance( n, 1, samples, 1 );
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console.log( 'Sample Mean:', sampleMean );
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console.log( 'Sample Variance:', sampleVariance );
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// Compare sample statistics to theoretical values:
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console.log( 'Difference in Mean:', abs( theoreticalMean - sampleMean ) );
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console.log( 'Difference in Variance:', abs( theoreticalVariance - sampleVariance ) );
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// Demonstrate the relationship with the Rayleigh distribution when k=2:
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var rayleighPDF = rayleigh.pdf.factory( 1.0 );
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var rayleighCDF = rayleigh.cdf.factory( 1.0 );
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// Compute Rayleigh PDF and CDF for each x:
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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:
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var maxDiffPDF = 0.0;
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var maxDiffCDF = 0.0;
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var diffPDF;
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var diffCDF;
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var i;
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for ( i = 0; i < x.length; i++ ) {
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diffPDF = abs( pdf[ i ] - rayleighPDFValues[ i ] );
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if ( diffPDF > maxDiffPDF ) {
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maxDiffPDF = diffPDF;
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}
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diffCDF = abs( cdf[ i ] - rayleighCDFValues[ i ] );
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if ( diffCDF > maxDiffCDF ) {
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maxDiffCDF = diffCDF;
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}
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}
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console.log( 'Maximum difference between Chi(k=2) PDF and Rayleigh PDF:', maxDiffPDF );
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console.log( 'Maximum difference between Chi(k=2) CDF and Rayleigh CDF:', maxDiffCDF );

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