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

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</details>

# Gamma

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

> Gamma 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-gamma-ctor
```

</section>

<section class="usage">

## Usage

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

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

Returns a [gamma][gamma-distribution] distribution object.

```javascript
var gamma = new Gamma();

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

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

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

* * *

## gamma

A [gamma][gamma-distribution] distribution object has the following properties and methods...

### Writable Properties

#### gamma.alpha

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

```javascript
var gamma = new Gamma();

var alpha = gamma.alpha;
// returns 1.0

gamma.alpha = 3.0;

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

#### gamma.beta

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var b = gamma.beta;
// returns 4.0

gamma.beta = 3.0;

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

* * *

### Computed Properties

#### Gamma.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var entropy = gamma.entropy;
// returns ~-0.462
```

#### Gamma.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var kurtosis = gamma.kurtosis;
// returns 1.5
```

#### Gamma.prototype.mean

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

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var mu = gamma.mean;
// returns ~0.333
```

#### Gamma.prototype.mode

Returns the [mode][mode].

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var mode = gamma.mode;
// returns 0.25
```

#### Gamma.prototype.skewness

Returns the [skewness][skewness].

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var skewness = gamma.skewness;
// returns 1.0
```

#### Gamma.prototype.stdev

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

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var s = gamma.stdev;
// returns ~0.167
```

#### Gamma.prototype.variance

Returns the [variance][variance].

```javascript
var gamma = new Gamma( 4.0, 12.0 );

var s2 = gamma.variance;
// returns ~0.028
```

* * *

### Methods

#### Gamma.prototype.cdf( x )

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.cdf( 0.5 );
// returns ~0.594
```

#### Gamma.prototype.logcdf( x )

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.logcdf( 0.5 );
// returns ~-0.521
```

#### Gamma.prototype.logpdf( x )

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.logpdf( 0.8 );
// returns ~-0.651
```

#### Gamma.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.mgf( 0.5 );
// returns ~1.306
```

#### Gamma.prototype.pdf( x )

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.pdf( 0.8 );
// returns ~0.522
```

#### Gamma.prototype.quantile( p )

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

```javascript
var gamma = new Gamma( 2.0, 4.0 );

var y = gamma.quantile( 0.5 );
// returns ~0.42

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

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var gamma = new Gamma( 2.0, 4.0 );

var mu = gamma.mean;
// returns 0.5

var mode = gamma.mode;
// returns 0.25

var s2 = gamma.variance;
// returns 0.125

var y = gamma.cdf( 0.8 );
// returns ~0.829
```

</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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[umd]: https://github.com/umdjs/umd
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-gamma-ctor/main/LICENSE

[gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution

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

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function

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

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

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[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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