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

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# Chi

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

> Chi 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-chi-ctor
```

</section>

<section class="usage">

## Usage

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

#### Chi( \[k] )

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

```javascript
var chi = new Chi();

var mu = chi.mean;
// returns ~0.798
```

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

```javascript
var chi = new Chi( 4.0 );

var mu = chi.mean;
// returns ~1.88
```

* * *

## chi

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

### Writable Properties

#### chi.k

Degrees of freedom of the distribution. `k` **must** be a positive number.

```javascript
var chi = new Chi( 2.0 );

var k = chi.k;
// returns 2.0

chi.k = 3.0;

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

* * *

### Computed Properties

#### Chi.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var chi = new Chi( 4.0 );

var entropy = chi.entropy;
// returns ~1.019
```

#### Chi.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var chi = new Chi( 4.0 );

var kurtosis = chi.kurtosis;
// returns ~0.059
```

#### Chi.prototype.mean

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

```javascript
var chi = new Chi( 4.0 );

var mu = chi.mean;
// returns ~1.88
```

#### Chi.prototype.mode

Returns the [mode][mode].

```javascript
var chi = new Chi( 4.0 );

var mode = chi.mode;
// returns ~1.732
```

#### Chi.prototype.skewness

Returns the [skewness][skewness].

```javascript
var chi = new Chi( 4.0 );

var skewness = chi.skewness;
// returns ~0.406
```

#### Chi.prototype.stdev

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

```javascript
var chi = new Chi( 4.0 );

var s = chi.stdev;
// returns ~0.682
```

#### Chi.prototype.variance

Returns the [variance][variance].

```javascript
var chi = new Chi( 4.0 );

var s2 = chi.variance;
// returns ~0.466
```

* * *

### Methods

#### Chi.prototype.cdf( x )

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

```javascript
var chi = new Chi( 2.0 );

var y = chi.cdf( 0.5 );
// returns ~0.118
```

#### Chi.prototype.logpdf( x )

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

```javascript
var chi = new Chi( 2.0 );

var y = chi.logpdf( 0.8 );
// returns ~-0.543
```

#### Chi.prototype.pdf( x )

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

```javascript
var chi = new Chi( 2.0 );

var y = chi.pdf( 0.8 );
// returns ~0.581
```

#### Chi.prototype.quantile( p )

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

```javascript
var chi = new Chi( 2.0 );

var y = chi.quantile( 0.5 );
// returns ~1.177

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

var chi = new Chi( 2.0 );

var mu = chi.mean;
// returns ~1.253

var mode = chi.mode;
// returns 1.0

var s2 = chi.variance;
// returns ~0.429

var y = chi.cdf( 0.8 );
// returns ~0.274
```

</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-chi-ctor/main/LICENSE

[chi-distribution]: https://en.wikipedia.org/wiki/Chi_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

[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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