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# npm

## @stdlib/stats-base-dists-kumaraswamy-pdf

0.0.6 • Public • Published

# Probability Density Function

The probability density function (PDF) 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-pdf`

## Usage

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

#### pdf( x, a, b )

Evaluates the probability density function (PDF) for a Kumaraswamy's double bounded distribution with parameters `a` (first shape parameter) and `b` (second shape parameter).

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

y = pdf( 0.5, 2.0, 4.0 );
// returns ~1.688

y = pdf( 0.2, 2.0, 2.0 );
// returns ~0.768

y = pdf( 0.8, 4.0, 4.0 );
// returns ~1.686

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

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

y = pdf( 1.5, 4.0, 2.0 );
// returns 0.0

y = pdf( +Infinity, 4.0, 2.0 );
// 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 `a <= 0`, the function returns `NaN`.

```var y = pdf( 2.0, -1.0, 0.5 );
// returns NaN

y = pdf( 2.0, 0.0, 0.5 );
// returns NaN```

If provided `b <= 0`, the function returns `NaN`.

```var y = pdf( 2.0, 0.5, -1.0 );
// returns NaN

y = pdf( 2.0, 0.5, 0.0 );
// returns NaN```

#### pdf.factory( a, b )

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

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

var y = mypdf( 0.8 );
// returns ~0.86

y = mypdf( 0.3 );
// returns ~0.679```

## Examples

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

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 = pdf( 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.

## Keywords

### Install

`npm i @stdlib/stats-base-dists-kumaraswamy-pdf`

stdlib.io

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0.0.6

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