Probability Density Function

F distribution probability density function (PDF).

The probability density function (PDF) for a F 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

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

Usage

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

pdf( x, d1, d2 )

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

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.

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.

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.

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

var mypdf = pdf.factory( 6.0, 7.0 );
var y = mypdf( 7.0 );
// returns ~0.004

y = mypdf( 2.0 );
// returns ~0.166

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    x = randu() * 4.0;
    d1 = randu() * 10.0;
    d2 = randu() * 10.0;
    y = pdf( 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.

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Copyright

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