# @stdlib/stats-base-dists-betaprime-cdf

0.2.2 • Public • Published

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# 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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-betaprime-cdf`

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