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

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# ChiSquare

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

> Chi-squared 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-chisquare-ctor
```

</section>

<section class="usage">

## Usage

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

#### ChiSquare( \[k] )

Returns an [chi-squared][chisquare-distribution] distribution object.

```javascript
var chisquare = new ChiSquare();

var mu = chisquare.mean;
// returns 1.0
```

By default, `k = 1.0`. To create a distribution having a different degrees of freedom `k`, provide a parameter value.

```javascript
var chisquare = new ChiSquare( 4.0 );

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

* * *

## chisquare

A [chi-squared][chisquare-distribution] distribution object has the following properties and methods...

### Writable Properties

#### chisquare.k

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

```javascript
var chisquare = new ChiSquare( 2.0 );

var k = chisquare.k;
// returns 2.0

chisquare.k = 3.0;

k = chisquare.k;
// returns 3.0
```

* * *

### Computed Properties

#### ChiSquare.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var chisquare = new ChiSquare( 4.0 );

var entropy = chisquare.entropy;
// returns ~2.27
```

#### ChiSquare.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var chisquare = new ChiSquare( 4.0 );

var kurtosis = chisquare.kurtosis;
// returns 3.0
```

#### ChiSquare.prototype.mean

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

```javascript
var chisquare = new ChiSquare( 4.0 );

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

#### ChiSquare.prototype.median

Returns the [median][median].

```javascript
var chisquare = new ChiSquare( 4.0 );

var median = chisquare.median;
// returns ~3.357
```

#### ChiSquare.prototype.mode

Returns the [mode][mode].

```javascript
var chisquare = new ChiSquare( 4.0 );

var mode = chisquare.mode;
// returns 2.0
```

#### ChiSquare.prototype.skewness

Returns the [skewness][skewness].

```javascript
var chisquare = new ChiSquare( 4.0 );

var skewness = chisquare.skewness;
// returns ~1.414
```

#### ChiSquare.prototype.stdev

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

```javascript
var chisquare = new ChiSquare( 4.0 );

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

#### ChiSquare.prototype.variance

Returns the [variance][variance].

```javascript
var chisquare = new ChiSquare( 4.0 );

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

* * *

### Methods

#### ChiSquare.prototype.cdf( x )

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

```javascript
var chisquare = new ChiSquare( 2.0 );

var y = chisquare.cdf( 0.5 );
// returns ~0.221
```

#### ChiSquare.prototype.mgf( t )

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

```javascript
var chisquare = new ChiSquare( 2.0 );

var y = chisquare.mgf( 0.2 );
// returns ~1.667
```

#### ChiSquare.prototype.pdf( x )

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

```javascript
var chisquare = new ChiSquare( 2.0 );

var y = chisquare.pdf( 0.8 );
// returns ~0.335
```

#### ChiSquare.prototype.quantile( p )

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

```javascript
var chisquare = new ChiSquare( 2.0 );

var y = chisquare.quantile( 0.5 );
// returns ~1.386

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

</section>

<!-- /.usage -->

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var chisquare = new ChiSquare( 2.0 );

var mu = chisquare.mean;
// returns 2.0

var mode = chisquare.mode;
// returns 0.0

var s2 = chisquare.variance;
// returns 4.0

var y = chisquare.cdf( 0.8 );
// returns ~0.33
```

</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].

</section>

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

[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_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

[median]: https://en.wikipedia.org/wiki/Median

[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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