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Chi distribution.
import chi from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-chi@esm/index.mjs';You can also import the following named exports from the package:
import { Chi, cdf, entropy, kurtosis, logpdf, mean, mode, pdf, quantile, skewness, stdev, variance } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-chi@esm/index.mjs';Chi distribution.
var dist = chi;
// returns {...}The namespace contains the following distribution functions:
cdf( x, k ): Chi distribution cumulative distribution function.logpdf( x, k ): evaluate the natural logarithm of the probability density function (PDF) for a chi distribution .pdf( x, k ): Chi distribution probability density function (PDF).quantile( p, k ): Chi distribution quantile function.
The namespace contains the following functions for calculating distribution properties:
entropy( k ): Chi distribution differential entropy.kurtosis( k ): Chi distribution excess kurtosis.mean( k ): Chi distribution expected value.mode( k ): Chi distribution mode.skewness( k ): Chi distribution skewness.stdev( k ): Chi distribution standard deviation.variance( k ): Chi distribution variance.
The namespace contains a constructor function for creating a Chi distribution object.
Chi( [k] ): Chi distribution constructor.
var Chi = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-chi' ).Chi;
var dist = new Chi( 4.0 );
var mu = dist.mean;
// returns ~1.88<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">
var chiRandomFactory = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-chi' ).factory;
import filledarrayBy from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-filled-by@esm/index.mjs';
import variance from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-variance@esm/index.mjs';
import linspace from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-base-linspace@esm/index.mjs';
import rayleigh from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-rayleigh@esm/index.mjs';
import absdiff from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-utils-absolute-difference@esm/index.mjs';
import mean from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-mean@esm/index.mjs';
import abs from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-abs@esm/index.mjs';
import max from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-max@esm/index.mjs';
import chi from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-chi@esm/index.mjs';
// Define the degrees of freedom parameter:
var k = 2;
// Generate an array of x values:
var x = linspace( 0, 10, 100 );
// Compute the PDF for each x:
var chiPDF = chi.pdf.factory( k );
var pdf = filledarrayBy( x.length, 'float64', chiPDF );
// Compute the CDF for each x:
var chiCDF = chi.cdf.factory( k );
var cdf = filledarrayBy( x.length, 'float64', chiCDF );
// Output the PDF and CDF values:
console.log( 'x values: ', x );
console.log( 'PDF values: ', pdf );
console.log( 'CDF values: ', cdf );
// Compute statistical properties:
var theoreticalMean = chi.mean( k );
var theoreticalVariance = chi.variance( k );
var theoreticalSkewness = chi.skewness( k );
var theoreticalKurtosis = chi.kurtosis( k );
console.log( 'Theoretical Mean: ', theoreticalMean );
console.log( 'Theoretical Variance: ', theoreticalVariance );
console.log( 'Skewness: ', theoreticalSkewness );
console.log( 'Kurtosis: ', theoreticalKurtosis );
// Generate random samples from the Chi distribution:
var rchi = chiRandomFactory( k );
var n = 1000;
var samples = filledarrayBy( n, 'float64', rchi );
// Compute sample mean and variance:
var sampleMean = mean( n, samples, 1 );
var sampleVariance = variance( n, 1, samples, 1 );
console.log( 'Sample Mean: ', sampleMean );
console.log( 'Sample Variance: ', sampleVariance );
// Compare sample statistics to theoretical values:
console.log( 'Difference in Mean: ', abs( theoreticalMean - sampleMean ) );
console.log( 'Difference in Variance: ', abs( theoreticalVariance - sampleVariance ) );
// Demonstrate the relationship with the Rayleigh distribution when k=2:
var rayleighPDF = rayleigh.pdf.factory( 1.0 );
var rayleighCDF = rayleigh.cdf.factory( 1.0 );
// Compute Rayleigh PDF and CDF for each x:
var rayleighPDFValues = filledarrayBy( x.length, 'float64', rayleighPDF );
var rayleighCDFValues = filledarrayBy( x.length, 'float64', rayleighCDF );
// 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 = absdiff( pdf[ i ], rayleighPDFValues[ i ] );
maxDiffPDF = max( maxDiffPDF, diffPDF );
diffCDF = absdiff( cdf[ i ], rayleighCDFValues[ i ] );
maxDiffCDF = max( 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 );
</script>
</body>
</html>This package is part of stdlib, a standard library with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.