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

Standard library statistical functions.

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# Kumaraswamy

> Kumaraswamy's double bounded distribution constructor.

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## 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
```

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* * *

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## 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
```

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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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