@stdlib/stats-base-dists-f-cdf
v0.2.3TypeScript
F distribution cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
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Published by The Stdlib Authors
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Cumulative Distribution Function
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> [F][f-distribution] distribution [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [F][f-distribution] random variable is
where d1 is the numerator degrees of freedom, d2 is the denominator degrees of freedom and I_{x}(a,b) is the [lower regularized incomplete beta function][@stdlib/math/base/special/betainc].
Installation
``bash`
npm install @stdlib/stats-base-dists-f-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-f-cdf' );
#### cdf( x, d1, d2 )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [F][f-distribution] distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).
`javascript
var y = cdf( 2.0, 1.0, 1.0 );
// returns ~0.608
y = cdf( 2.0, 8.0, 4.0 );
// returns ~0.737
y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0
y = cdf( 0.0, 4.0, 4.0 );
// returns 0.0
y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = cdf( NaN, 1.0, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 1.0, NaN );
// returns NaN
`
If provided d1 <= 0, the function returns NaN.
`javascript
var y = cdf( 2.0, -1.0, 0.5 );
// returns NaN
y = cdf( 2.0, 0.0, 0.5 );
// returns NaN
`
If provided d2 <= 0, the function returns NaN.
`javascript
var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN
y = cdf( 2.0, 0.5, 0.0 );
// returns NaN
`
#### cdf.factory( d1, d2 )
Returns a function for evaluating the [cumulative distribution function][cdf] of an [F][f-distribution] distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).
`javascript
var mycdf = cdf.factory( 10.0, 2.0 );
var y = mycdf( 10.0 );
// returns ~0.906
y = mycdf( 8.0 );
// returns ~0.884
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-f-cdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 10.0, 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, cdf );
`
*
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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[stdlib]: https://github.com/stdlib-js/stdlib
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[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-cdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-f-cdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-f-cdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-f-cdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-f-cdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-f-cdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-f-cdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-f-cdf/main/LICENSE
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[f-distribution]: https://en.wikipedia.org/wiki/F_distribution
[@stdlib/math/base/special/betainc]: https://www.npmjs.com/package/@stdlib/math-base-special-betainc