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stats-base-dists-chi

Chi distribution.

https://github.com/stdlib-js/stats-base-dists-chi

Science Score: 44.0%

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Keywords

chi continuous dist distribution javascript lib library node node-js nodejs prob probability standard statistics stats stdlib univariate
Last synced: 6 months ago · JSON representation ·

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Chi distribution.

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Statistics
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Topics
chi continuous dist distribution javascript lib library node node-js nodejs prob probability standard statistics stats stdlib univariate
Created over 4 years ago · Last pushed 8 months ago
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README.md

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Chi

NPM version Build Status Coverage Status <!-- dependencies -->

Chi distribution.

## Installation ```bash npm install @stdlib/stats-base-dists-chi ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage ```javascript var chi = require( '@stdlib/stats-base-dists-chi' ); ``` #### chi Chi distribution. ```javascript var dist = chi; // returns {...} ``` The namespace contains the following distribution functions:
- [`cdf( x, k )`][@stdlib/stats/base/dists/chi/cdf]: Chi distribution cumulative distribution function. - [`logpdf( x, k )`][@stdlib/stats/base/dists/chi/logpdf]: evaluate the natural logarithm of the probability density function (PDF) for a chi distribution. - [`pdf( x, k )`][@stdlib/stats/base/dists/chi/pdf]: Chi distribution probability density function (PDF). - [`quantile( p, k )`][@stdlib/stats/base/dists/chi/quantile]: Chi distribution quantile function.
The namespace contains the following functions for calculating distribution properties:
- [`entropy( k )`][@stdlib/stats/base/dists/chi/entropy]: Chi distribution differential entropy. - [`kurtosis( k )`][@stdlib/stats/base/dists/chi/kurtosis]: Chi distribution excess kurtosis. - [`mean( k )`][@stdlib/stats/base/dists/chi/mean]: Chi distribution expected value. - [`mode( k )`][@stdlib/stats/base/dists/chi/mode]: Chi distribution mode. - [`skewness( k )`][@stdlib/stats/base/dists/chi/skewness]: Chi distribution skewness. - [`stdev( k )`][@stdlib/stats/base/dists/chi/stdev]: Chi distribution standard deviation. - [`variance( k )`][@stdlib/stats/base/dists/chi/variance]: Chi distribution variance.
The namespace contains a constructor function for creating a [Chi][chi-distribution] distribution object.
- [`Chi( [k] )`][@stdlib/stats/base/dists/chi/ctor]: Chi distribution constructor.
```javascript var Chi = require( '@stdlib/stats-base-dists-chi' ).Chi; var dist = new Chi( 4.0 ); var mu = dist.mean; // returns ~1.88 ```
## Examples ```javascript var chiRandomFactory = require( '@stdlib/random-base-chi' ).factory; var filledarrayBy = require( '@stdlib/array-filled-by' ); var variance = require( '@stdlib/stats-strided-variance' ); var linspace = require( '@stdlib/array-base-linspace' ); var rayleigh = require( '@stdlib/stats-base-dists-rayleigh' ); var absdiff = require( '@stdlib/math-base-utils-absolute-difference' ); var mean = require( '@stdlib/stats-strided-mean' ); var abs = require( '@stdlib/math-base-special-abs' ); var max = require( '@stdlib/math-base-special-max' ); var chi = require( '@stdlib/stats-base-dists-chi' ); // 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 ); ```
* * * ## Notice This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, 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][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Standard library for JavaScript.

Citation (CITATION.cff) 

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
  metadata from this file.

type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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