Cumulative Distribution Function

Kumaraswamy's double bounded distribution cumulative distribution function.

The cumulative distribution function for a Kumaraswamy's double bounded random variable is

where a > 0 is the first shape parameter and b > 0 is the second shape parameter.

Installation

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

Usage

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

cdf( x, a, b )

Evaluates the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

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

y = cdf( 0.5, 2.0, 4.0 );
// returns ~0.684

y = cdf( 0.2, 2.0, 2.0 );
// returns ~0.078

y = cdf( 0.8, 4.0, 4.0 );
// returns ~0.878

y = cdf( -0.5, 4.0, 2.0 );
// returns 0.0

y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0

y = cdf( 1.5, 4.0, 2.0 );
// returns 1.0

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 a <= 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 b <= 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( a, b )

Returns a function for evaluating the cumulative distribution function for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

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

var y = mycdf( 0.8 );
// returns ~0.675

y = mycdf( 0.3 );
// returns ~0.327

Examples

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

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu();
    a = ( randu()*5.0 ) + EPS;
    b = ( randu()*5.0 ) + EPS;
    y = cdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, F(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.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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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.