Probability Density Function

Beta prime distribution probability density function (PDF).

The probability density function (PDF) for a beta prime random variable is

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Installation

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

Usage

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

pdf( x, alpha, beta )

Evaluates the probability density function (PDF) for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = pdf( 0.5, 0.5, 1.0 );
// returns ~0.385

y = pdf( 0.1, 1.0, 1.0 );
// returns ~0.826

y = pdf( 0.8, 4.0, 2.0 );
// returns ~0.301

If provided a x <= 0, the function returns 0.

var y = pdf( -0.1, 1.0, 1.0 );
// returns 0.0

y = pdf( 0.0, 1.0, 1.0 );
// 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 alpha <= 0, the function returns NaN.

var y = pdf( 0.5, 0.0, 1.0 );
// returns NaN

y = pdf( 0.5, -1.0, 1.0 );
// returns NaN

If provided beta <= 0, the function returns NaN.

var y = pdf( 0.5, 1.0, 0.0 );
// returns NaN

y = pdf( 0.5, 1.0, -1.0 );
// returns NaN

pdf.factory( alpha, beta )

Returns a function for evaluating the PDF for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var mypdf = pdf.factory( 0.5, 0.5 );

var y = mypdf( 0.8 );
// returns ~0.198

y = mypdf( 0.3 );
// returns ~0.447

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var pdf = require( '@stdlib/stats-base-dists-betaprime-pdf' );

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu();
    alpha = ( randu()*5.0 ) + EPS;
    beta = ( randu()*5.0 ) + EPS;
    y = pdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, f(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.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.