@stdlib/stats-base-dists-kumaraswamy-ctor/README.md

Kumaraswamy's double bounded distribution constructor.

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# Kumaraswamy

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> Kumaraswamy's double bounded distribution constructor.

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<section class="intro">

</section>

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<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-kumaraswamy-ctor
```

</section>

<section class="usage">

## Usage

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

#### Kumaraswamy( \[a, b] )

Returns a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution object.

```javascript
var kumaraswamy = new Kumaraswamy();

var mu = kumaraswamy.mean;
// returns 0.5
```

By default, `a = 1.0` and `b = 1.0`. To create a distribution having a different `a` (first shape parameter) and `b` (second shape parameter), provide the corresponding arguments.

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var mu = kumaraswamy.mean;
// returns ~0.406
```

* * *

## kumaraswamy

A [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution object has the following properties and methods...

### Writable Properties

#### kumaraswamy.a

First shape parameter of the distribution. `a` **must** be a positive number.

```javascript
var kumaraswamy = new Kumaraswamy();

var a = kumaraswamy.a;
// returns 1.0

kumaraswamy.a = 3.0;

a = kumaraswamy.a;
// returns 3.0
```

#### kumaraswamy.b

Second shape parameter of the distribution. `b` **must** be a positive number.

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var b = kumaraswamy.b;
// returns 4.0

kumaraswamy.b = 3.0;

b = kumaraswamy.b;
// returns 3.0
```

* * *

### Computed Properties

#### Kumaraswamy.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );

var kurtosis = kumaraswamy.kurtosis;
// returns ~2.704
```

#### Kumaraswamy.prototype.mean

Returns the [expected value][expected-value].

```javascript
var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );

var mu = kumaraswamy.mean;
// returns ~0.481
```

#### Kumaraswamy.prototype.mode

Returns the [mode][mode].

```javascript
var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );

var mode = kumaraswamy.mode;
// returns ~0.503
```

#### Kumaraswamy.prototype.skewness

Returns the [skewness][skewness].

```javascript
var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );

var skewness = kumaraswamy.skewness;
// returns ~-0.201
```

#### Kumaraswamy.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );

var s = kumaraswamy.stdev;
// returns ~0.13
```

#### Kumaraswamy.prototype.variance

Returns the [variance][variance].

```javascript
var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );

var s2 = kumaraswamy.variance;
// returns ~0.017
```

* * *

### Methods

#### Kumaraswamy.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var y = kumaraswamy.cdf( 0.5 );
// returns ~0.684
```

#### Kumaraswamy.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var y = kumaraswamy.logcdf( 0.5 );
// returns ~-0.38
```

#### Kumaraswamy.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var y = kumaraswamy.logpdf( 0.8 );
// returns ~-1.209
```

#### Kumaraswamy.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var y = kumaraswamy.pdf( 0.8 );
// returns ~0.299
```

#### Kumaraswamy.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var y = kumaraswamy.quantile( 0.5 );
// returns ~0.399

y = kumaraswamy.quantile( 1.9 );
// returns NaN
```

</section>

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</section>

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* * *

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

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

var kumaraswamy = new Kumaraswamy( 2.0, 4.0 );

var mu = kumaraswamy.mean;
// returns ~0.406

var mode = kumaraswamy.mode;
// returns ~0.378

var s2 = kumaraswamy.variance;
// returns ~0.035

var y = kumaraswamy.cdf( 0.8 );
// returns ~0.983
```

</section>

<!-- /.examples -->

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* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2024. The Stdlib [Authors][stdlib-authors].

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[kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

[variance]: https://en.wikipedia.org/wiki/Variance

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