https://github.com/stdlib-js/stats-base-dists-gamma-ctor
Gamma distribution constructor.
https://github.com/stdlib-js/stats-base-dists-gamma-ctor
cdf class constructor ctor dist distribution gamma javascript node node-js nodejs object pdf prob probability properties quantile statistics stats stdlib
Last synced: 6 months ago
JSON representation
Gamma distribution constructor.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-gamma-ctor
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:38:41.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-02-20T00:25:18.000Z (8 months ago)
- Last Synced: 2025-04-14T16:18:56.894Z (6 months ago)
- Topics: cdf, class, constructor, ctor, dist, distribution, gamma, javascript, node, node-js, nodejs, object, pdf, prob, probability, properties, quantile, statistics, stats, stdlib
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 4.2 MB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# Gamma
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Gamma distribution constructor.
## Installation
```bash
npm install @stdlib/stats-base-dists-gamma-ctor
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## 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
```
* * *
## Examples
```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
```
* * *
## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-gamma-ctor.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-gamma-ctor
[test-image]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-gamma-ctor/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-gamma-ctor?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[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-gamma-ctor/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-gamma-ctor/blob/main/branches.md
[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