Cumulative Distribution Function

F distribution cumulative distribution function.

The cumulative distribution function for a F 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.

Installation

npm install @stdlib/stats-base-dists-f-cdf

Usage

var cdf = require( '@stdlib/stats-base-dists-f-cdf' );

cdf( x, d1, d2 )

Evaluates the cumulative distribution function (CDF) for a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

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.

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.

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.

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 of a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var mycdf = cdf.factory( 10.0, 2.0 );

var y = mycdf( 10.0 );
// returns ~0.906

y = mycdf( 8.0 );
// returns ~0.884

Examples

var randu = require( '@stdlib/random-base-randu' );
var cdf = require( '@stdlib/stats-base-dists-f-cdf' );

var d1;
var d2;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    d1 = randu() * 10.0;
    d2 = randu() * 10.0;
    y = cdf( x, d1, d2 );
    console.log( 'x: %d, d1: %d, d2: %d, F(x;d1,d2): %d', x.toFixed( 4 ), d1.toFixed( 4 ), d2.toFixed( 4 ), y.toFixed( 4 ) );
}

Notice

This package is part of 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, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.