Cumulative Distribution Function

Beta prime distribution cumulative distribution function.

The cumulative distribution function for a beta prime random variable is

where alpha > 0 is the first shape parameter, beta > 0 is the second shape parameter and I is the incomplete beta function.

Installation

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

Usage

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

cdf( x, alpha, beta )

Evaluates the cumulative distribution function (CDF) for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = cdf( 0.5, 1.0, 1.0 );
// returns ~0.333

y = cdf( 0.5, 2.0, 4.0 );
// returns ~0.539

y = cdf( 0.2, 2.0, 2.0 );
// returns ~0.074

y = cdf( 0.8, 4.0, 4.0 );
// returns ~0.38

y = cdf( -0.5, 4.0, 2.0 );
// 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 alpha <= 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 beta <= 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( alpha, beta )

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

var mycdf = cdf.factory( 0.5, 0.5 );

var y = mycdf( 0.8 );
// returns ~0.465

y = mycdf( 0.3 );
// returns ~0.319

Examples

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

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 = cdf( 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.