@stdlib/stats-base-dists-f-pdf
v0.2.3TypeScript
F distribution probability density function (PDF).
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Published by The Stdlib Authors
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Probability Density Function
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> [F][f-distribution] distribution probability density function (PDF).
The [probability density function][pdf] (PDF) for a [F][f-distribution] random variable is
where d1 is the numerator degrees of freedom and d2 is the denominator degrees of freedom and B is the Beta function.
Installation
``bash`
npm install @stdlib/stats-base-dists-f-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-f-pdf' );
#### pdf( x, d1, d2 )
Evaluates the [probability density function][pdf] (PDF) for a [F][f-distribution] distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).
`javascript
var y = pdf( 2.0, 0.5, 1.0 );
// returns ~0.057
y = pdf( 0.1, 1.0, 1.0 );
// returns ~0.915
y = pdf( -1.0, 4.0, 2.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pdf( NaN, 1.0, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 1.0, NaN );
// returns NaN
`
If provided d1 <= 0, the function returns NaN.
`javascript
var y = pdf( 2.0, 0.0, 1.0 );
// returns NaN
y = pdf( 2.0, -1.0, 1.0 );
// returns NaN
`
If provided d2 <= 0, the function returns NaN.
`javascript
var y = pdf( 2.0, 1.0, 0.0 );
// returns NaN
y = pdf( 2.0, 1.0, -1.0 );
// returns NaN
`
#### pdf.factory( d1, d2 )
Returns a function for evaluating the [PDF][pdf] of an [F][f-distribution] distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).
`javascript
var mypdf = pdf.factory( 6.0, 7.0 );
var y = mypdf( 7.0 );
// returns ~0.004
y = mypdf( 2.0 );
// returns ~0.166
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pdf = require( '@stdlib/stats-base-dists-f-pdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 4.0, opts );
var d1 = uniform( 10, 0.0, 10.0, opts );
var d2 = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, d1: %0.4f, d2: %0.4f, f(x;d1,d2): %0.4f', x, d1, d2, pdf );
`
*
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]
---
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-f-pdf
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[test-url]: https://github.com/stdlib-js/stats-base-dists-f-pdf/actions/workflows/test.yml?query=branch:v0.2.3
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-f-pdf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-f-pdf?branch=main
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[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-f-pdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-f-pdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-f-pdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-f-pdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-f-pdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-f-pdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-f-pdf/blob/main/branches.md
[f-distribution]: https://en.wikipedia.org/wiki/F_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function