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

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# Inverse Gamma

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

> Inverse gamma distribution constructor.

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<section class="intro">

</section>

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<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

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

Returns an [inverse gamma][invgamma-distribution] distribution object.

```javascript
var invgamma = new InvGamma();

var mode = invgamma.mode;
// returns 0.5
```

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 invgamma = new InvGamma( 2.0, 4.0 );

var mu = invgamma.mean;
// returns 4.0
```

* * *

## invgamma

An [inverse gamma][invgamma-distribution] distribution object has the following properties and methods...

### Writable Properties

#### invgamma.alpha

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

```javascript
var invgamma = new InvGamma();

var alpha = invgamma.alpha;
// returns 1.0

invgamma.alpha = 3.0;

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

#### invgamma.beta

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var b = invgamma.beta;
// returns 4.0

invgamma.beta = 3.0;

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

* * *

### Computed Properties

#### InvGamma.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var invgamma = new InvGamma( 6.0, 12.0 );

var kurtosis = invgamma.kurtosis;
// returns 19.0
```

#### InvGamma.prototype.mean

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

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var mu = invgamma.mean;
// returns 4.0
```

#### InvGamma.prototype.mode

Returns the [mode][mode].

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var mode = invgamma.mode;
// returns 2.4
```

#### InvGamma.prototype.skewness

Returns the [skewness][skewness].

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var skewness = invgamma.skewness;
// returns ~5.657
```

#### InvGamma.prototype.stdev

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

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var s = invgamma.stdev;
// returns ~2.828
```

#### InvGamma.prototype.variance

Returns the [variance][variance].

```javascript
var invgamma = new InvGamma( 4.0, 12.0 );

var s2 = invgamma.variance;
// returns 8.0
```

* * *

### Methods

#### InvGamma.prototype.cdf( x )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.cdf( 0.5 );
// returns ~0.003
```

#### InvGamma.prototype.logpdf( x )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.logpdf( 0.8 );
// returns ~-1.558
```

#### InvGamma.prototype.pdf( x )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.pdf( 0.8 );
// returns ~0.211
```

#### InvGamma.prototype.quantile( p )

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

```javascript
var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.quantile( 0.5 );
// returns ~2.383

y = invgamma.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 InvGamma = require( '@stdlib/stats-base-dists-invgamma-ctor' );

var invgamma = new InvGamma( 3.0, 4.0 );

var mu = invgamma.mean;
// returns 2.0

var mode = invgamma.mode;
// returns 1.0

var s2 = invgamma.variance;
// returns 4.0

var y = invgamma.cdf( 0.8 );
// returns ~0.125
```

</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

[![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-invgamma-ctor/main/LICENSE

[invgamma-distribution]: https://en.wikipedia.org/wiki/Inverse-gamma_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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