stdlib-js
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Cumulative Distribution Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
[Beta prime][betaprime-distribution] distribution [cumulative distribution function][cdf].
alpha > 0 is the first shape parameter, beta > 0 is the second shape parameter and I is the [incomplete beta function][incomplete-beta].
bash
npm install @stdlib/stats-base-dists-betaprime-cdf
javascript
var cdf = require( '@stdlib/stats-base-dists-betaprime-cdf' );
#### cdf( x, alpha, beta )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [beta prime][betaprime-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).
javascript
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.
javascript
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.
javascript
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.
javascript
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][cdf] for a [beta prime][betaprime-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).
javascript
var mycdf = cdf.factory( 0.5, 0.5 );
var y = mycdf( 0.8 );
// returns ~0.465
y = mycdf( 0.3 );
// returns ~0.319
javascript
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 ) );
}
