@stdlib/stats/base/dists/chi/skewness/README.md

Standard library statistical functions.

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# Skewness

> [Chi][chi-distribution] distribution [skewness][skewness].

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The [skewness][skewness] for a [chi][chi-distribution] random variable with degrees of freedom.`k` is

<!-- <equation class="equation" label="eq:chi_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{\mu}{\sigma^{3}}\,(1 - 2 \sigma^{2})" alt="Skewness for a chi distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{\mu}{\sigma^{3}}\,(1 - 2 \sigma^{2})" data-equation="eq:chi_skewness">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chi/skewness/docs/img/equation_chi_skewness.svg" alt="Skewness for a chi distribution.">
    <br>
</div>

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where `μ` is the mean of the distribution and `σ` its standard deviation.

</section>

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<section class="usage">

## Usage

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

#### skewness( k )

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

```javascript
var v = skewness( 9.0 );
// returns ~0.252

v = skewness( 0.5 );
// returns ~1.544
```

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

```javascript
var v = skewness( -1.0 );
// returns NaN
```

</section>

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

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</section>

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## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var skewness = require( '@stdlib/stats/base/dists/chi/skewness' );

var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = randu() * 20.0;
    v = skewness( k );
    console.log( 'k: %d, skew(X,k): %d', k.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

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</section>

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

[skewness]: https://en.wikipedia.org/wiki/Skewness

</section>

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