npm package: @stdlib/stats-base-dists-betaprime-ctor
Description: Beta prime distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Beta Prime

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Beta prime distribution constructor.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### BetaPrime( \[alpha, beta] )

Returns a [beta prime][betaprime-distribution] distribution object.

```javascript
var betaprime = new BetaPrime();

var mode = betaprime.mode;
// returns 0.0
```

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var mu = betaprime.mean;
// returns ~0.667
```

* * *

## betaprime

A [beta prime][betaprime-distribution] distribution object has the following properties and methods...

### Writable Properties

#### betaprime.alpha

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

```javascript
var betaprime = new BetaPrime();

var alpha = betaprime.alpha;
// returns 1.0

betaprime.alpha = 3.0;

alpha = betaprime.alpha;
// returns 3.0
```

#### betaprime.beta

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var b = betaprime.beta;
// returns 4.0

betaprime.beta = 3.0;

b = betaprime.beta;
// returns 3.0
```

* * *

### Computed Properties

#### BetaPrime.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var betaprime = new BetaPrime( 4.0, 12.0 );

var kurtosis = betaprime.kurtosis;
// returns ~5.764
```

#### BetaPrime.prototype.mean

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

```javascript
var betaprime = new BetaPrime( 4.0, 12.0 );

var mu = betaprime.mean;
// returns ~0.364
```

#### BetaPrime.prototype.mode

Returns the [mode][mode].

```javascript
var betaprime = new BetaPrime( 4.0, 12.0 );

var mode = betaprime.mode;
// returns ~0.231
```

#### BetaPrime.prototype.skewness

Returns the [skewness][skewness].

```javascript
var betaprime = new BetaPrime( 4.0, 12.0 );

var skewness = betaprime.skewness;
// returns ~1.724
```

#### BetaPrime.prototype.stdev

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

```javascript
var betaprime = new BetaPrime( 4.0, 12.0 );

var s = betaprime.stdev;
// returns ~0.223
```

#### BetaPrime.prototype.variance

Returns the [variance][variance].

```javascript
var betaprime = new BetaPrime( 4.0, 12.0 );

var s2 = betaprime.variance;
// returns ~0.05
```

* * *

### Methods

#### BetaPrime.prototype.cdf( x )

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.cdf( 0.5 );
// returns ~0.539
```

#### BetaPrime.prototype.logcdf( x )

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.logcdf( 0.5 );
// returns ~-0.618
```

#### BetaPrime.prototype.logpdf( x )

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.logpdf( 0.8 );
// returns ~-0.754
```

#### BetaPrime.prototype.pdf( x )

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.pdf( 0.8 );
// returns ~0.47
```

#### BetaPrime.prototype.quantile( p )

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

```javascript
var betaprime = new BetaPrime( 2.0, 4.0 );

var y = betaprime.quantile( 0.5 );
// returns ~0.457

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

</section>

<!-- /.usage -->

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<section class="notes">

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var betaprime = new BetaPrime( 2.0, 4.0 );

var mu = betaprime.mean;
// returns ~0.667

var mode = betaprime.mode;
// returns 0.2

var s2 = betaprime.variance;
// returns ~0.556

var y = betaprime.cdf( 0.8 );
// returns ~0.735
```

</section>

<!-- /.examples -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-betaprime-ctor/main/LICENSE

[betaprime-distribution]: https://en.wikipedia.org/wiki/Beta_prime_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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