npm package: @stdlib/stats-base-dists-chi-mean
Description: Chi distribution expected value.
Author: The Stdlib Authors
Latest version: 0.3.1

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<details>
  <summary>
    About stdlib...
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  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>
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</details>

# Mean

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

> [Chi][chi-distribution] distribution [expected value][expected-value].

<!-- 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">

The [expected value][expected-value] for a [chi][chi-distribution] random variable is

<!-- <equation class="equation" label="eq:chi_expectation" align="center" raw="\mathbb{E}\left[ X \right] = \sqrt{2}\,\frac{\Gamma((k+1)/2)}{\Gamma(k/2)}" alt="Expected value for a chi distribution."> -->

<div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = \sqrt{2}\,\frac{\Gamma((k+1)/2)}{\Gamma(k/2)}" data-equation="eq:chi_expectation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chi/mean/docs/img/equation_chi_expectation.svg" alt="Expected value for a chi distribution.">
    <br>
</div>

<!-- </equation> -->

where `k` is the degrees of freedom.

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-chi-mean
```

</section>

<section class="usage">

## Usage

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

#### mean( k )

Returns the [expected value][expected-value] of a [chi][chi-distribution] distribution with degrees of freedom `k`.

```javascript
var v = mean( 9.0 );
// returns ~2.918

v = mean( 0.5 );
// returns ~0.478
```

If provided `k < 0`, the function returns `NaN`.

```javascript
var v = mean( -1.0 );
// 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>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

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

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var mean = require( '@stdlib/stats-base-dists-chi-mean' );

var opts = {
    'dtype': 'float64'
};
var k = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'k: %0.4f, E(X;k): %0.4f', k, mean );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- 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 -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/chi/mean.h"
```

#### stdlib_base_dists_chi_mean( k )

Returns the [expected value][expected-value] of a [chi][chi-distribution] distribution with degrees of freedom `k`.

```c
double out = stdlib_base_dists_chi_mean( 2.0 );
// returns ~1.253
```

The function accepts the following arguments:

-   **k**: `[in] double` degrees of freedom.

```c
double stdlib_base_dists_chi_mean( const double k );
```

</section>

<!-- /.usage -->

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

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/chi/mean.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        k = random_uniform( 1.0, 10.0 );
        y = stdlib_base_dists_chi_mean( k );
        printf( "k: %lf, E(X,k): %lf\n", k, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="references">

</section>

<!-- /.references -->

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<section class="related">

</section>

<!-- /.related -->

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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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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

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

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

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

</section>

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