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# Kumaraswamy
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Kumaraswamy's double bounded distribution.
## Installation
```bash
npm install @stdlib/stats-base-dists-kumaraswamy
```
## Usage
```javascript
var kumaraswamy = require( '@stdlib/stats-base-dists-kumaraswamy' );
```
#### kumaraswamy
Kumaraswamy's double bounded distribution.
```javascript
var dist = kumaraswamy;
// returns {...}
```
The namespace contains the following distribution functions:
- [`cdf( x, a, b )`][@stdlib/stats/base/dists/kumaraswamy/cdf]: Kumaraswamy's double bounded distribution cumulative distribution function.
- [`logcdf( x, a, b )`][@stdlib/stats/base/dists/kumaraswamy/logcdf]: evaluate the natural logarithm of the cumulative distribution function for a Kumaraswamy's double bounded distribution.
- [`logpdf( x, a, b )`][@stdlib/stats/base/dists/kumaraswamy/logpdf]: evaluate the natural logarithm of the probability density function for a Kumaraswamy's double bounded distribution.
- [`pdf( x, a, b )`][@stdlib/stats/base/dists/kumaraswamy/pdf]: Kumaraswamy's double bounded distribution probability density function.
- [`quantile( p, a, b )`][@stdlib/stats/base/dists/kumaraswamy/quantile]: Kumaraswamy's double bounded distribution quantile function.
The namespace contains the following functions for calculating distribution properties:
- [`kurtosis( a, b )`][@stdlib/stats/base/dists/kumaraswamy/kurtosis]: Kumaraswamy's double bounded distribution excess kurtosis.
- [`mean( a, b )`][@stdlib/stats/base/dists/kumaraswamy/mean]: Kumaraswamy's double bounded distribution expected value.
- [`median( a, b )`][@stdlib/stats/base/dists/kumaraswamy/median]: Kumaraswamy's double bounded distribution median.
- [`mode( a, b )`][@stdlib/stats/base/dists/kumaraswamy/mode]: Kumaraswamy's double bounded distribution mode.
- [`skewness( a, b )`][@stdlib/stats/base/dists/kumaraswamy/skewness]: Kumaraswamy's double bounded distribution skewness.
- [`stdev( a, b )`][@stdlib/stats/base/dists/kumaraswamy/stdev]: Kumaraswamy's double bounded distribution standard deviation.
- [`variance( a, b )`][@stdlib/stats/base/dists/kumaraswamy/variance]: Kumaraswamy's double bounded distribution variance.
The namespace contains a constructor function for creating a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution object.
- [`Kumaraswamy( [a, b] )`][@stdlib/stats/base/dists/kumaraswamy/ctor]: Kumaraswamy's double bounded distribution constructor.
```javascript
var Kumaraswamy = require( '@stdlib/stats-base-dists-kumaraswamy' ).Kumaraswamy;
var dist = new Kumaraswamy( 2.0, 4.0 );
var y = dist.logpdf( 0.8 );
// returns ~-1.209
```
## Examples
```javascript
var kumaraswamy = require( '@stdlib/stats-base-dists-kumaraswamy' );
// Create a Kumaraswamy distribution object:
var a = 2.0;
var b = 5.0;
var dist = new kumaraswamy.Kumaraswamy( a, b );
// Calculate basic distribution properties:
console.log( 'Mean: %d', dist.mean );
console.log( 'Median: %d', dist.median );
console.log( 'Mode: %d', dist.mode );
console.log( 'Variance: %d', dist.variance );
// Evaluate the probability density function (PDF):
var x = 0.5;
var y = dist.pdf( x );
console.log( 'PDF at x = %d: %d', x, y );
// Evaluate the cumulative distribution function (CDF):
y = dist.cdf( x );
console.log( 'CDF at x = %d: %d', x, y );
// Evaluate the natural logarithm of PDF and CDF:
console.log( 'Log PDF at x = %d: %d', x, dist.logpdf( x ) );
console.log( 'Log CDF at x = %d: %d', x, dist.logcdf( x ) );
// Calculate the quantile for a given probability:
var p = 0.75;
x = dist.quantile( p );
console.log( 'Quantile at p = %d: %d', p, x );
// Use standalone distribution functions:
x = 0.3;
y = kumaraswamy.pdf( x, a, b );
console.log( 'Standalone PDF at x = %d: %d', x, y );
y = kumaraswamy.cdf( x, a, b );
console.log( 'Standalone CDF at x = %d: %d', x, y );
y = kumaraswamy.quantile( 0.9, a, b );
console.log( 'Standalone Quantile at p = 0.9: %d', y );
// Calculate additional distribution properties:
console.log( 'Kurtosis: %d', kumaraswamy.kurtosis( a, b ) );
console.log( 'Skewness: %d', kumaraswamy.skewness( a, b ) );
console.log( 'Standard Deviation: %d', kumaraswamy.stdev( a, b ) );
// Demonstrate the effect of different shape parameters:
console.log( '\nEffect of shape parameters:' );
var shapes = [
[ 0.5, 0.5 ],
[ 5.0, 1.0 ],
[ 1.0, 5.0 ],
[ 2.0, 2.0 ],
[ 10.0, 10.0 ]
];
var params;
var i;
for ( i = 0; i < shapes.length; i++ ) {
params = shapes[i];
console.log( '\na = %d, b = %d', params[0], params[1] );
console.log( 'Mean: %d', kumaraswamy.mean( params[0], params[1] ) );
console.log( 'Median: %d', kumaraswamy.median( params[0], params[1] ) );
console.log( 'Mode: %d', kumaraswamy.mode( params[0], params[1] ) );
console.log( 'Skewness: %d', kumaraswamy.skewness( params[0], params[1] ) );
}
```
* * *
## Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-kumaraswamy
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[test-url]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/actions/workflows/test.yml?query=branch:v0.3.1
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-kumaraswamy/main.svg
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[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-kumaraswamy/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-kumaraswamy/main/LICENSE
[kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution
[@stdlib/stats/base/dists/kumaraswamy/ctor]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-ctor
[@stdlib/stats/base/dists/kumaraswamy/kurtosis]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-kurtosis
[@stdlib/stats/base/dists/kumaraswamy/mean]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-mean
[@stdlib/stats/base/dists/kumaraswamy/median]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-median
[@stdlib/stats/base/dists/kumaraswamy/mode]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-mode
[@stdlib/stats/base/dists/kumaraswamy/skewness]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-skewness
[@stdlib/stats/base/dists/kumaraswamy/stdev]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-stdev
[@stdlib/stats/base/dists/kumaraswamy/variance]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-variance
[@stdlib/stats/base/dists/kumaraswamy/cdf]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-cdf
[@stdlib/stats/base/dists/kumaraswamy/logcdf]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-logcdf
[@stdlib/stats/base/dists/kumaraswamy/logpdf]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-logpdf
[@stdlib/stats/base/dists/kumaraswamy/pdf]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-pdf
[@stdlib/stats/base/dists/kumaraswamy/quantile]: https://www.npmjs.com/package/@stdlib/stats-base-dists-kumaraswamy-quantile