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# Standard Deviation

> [Beta][beta-distribution] distribution [standard deviation][stdev].

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The [standard deviation][stdev] for a [beta][beta-distribution] random variable is

<!-- <equation class="equation" label="eq:beta_stdev" align="center" raw="\sigma = (\alpha+\beta) \sqrt{\tfrac{\alpha\beta}{\alpha+\beta+1}}" alt="Standard deviation for a beta distribution."> -->

<div class="equation" align="center" data-raw-text="\sigma = (\alpha+\beta) \sqrt{\tfrac{\alpha\beta}{\alpha+\beta+1}}" data-equation="eq:beta_stdev">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/beta/stdev/docs/img/equation_beta_stdev.svg" alt="Standard deviation for a beta distribution.">
    <br>
</div>

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where `α > 0` is the first shape parameter and `β > 0` is the second shape parameter.

</section>

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<section class="usage">

## Usage

```javascript
var stdev = require( '@stdlib/stats/base/dists/beta/stdev' );
```

#### stdev( alpha, beta )

Returns the [standard deviation][stdev] of a [beta][beta-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).

```javascript
var v = stdev( 1.0, 1.0 );
// returns ~0.289

v = stdev( 4.0, 12.0 );
// returns ~0.105

v = stdev( 8.0, 2.0 );
// returns ~0.121
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var v = stdev( NaN, 2.0 );
// returns NaN

v = stdev( 2.0, NaN );
// returns NaN
```

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

```javascript
var v = stdev( 0.0, 1.0 );
// returns NaN

v = stdev( -1.0, 1.0 );
// returns NaN
```

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

```javascript
var v = stdev( 1.0, 0.0 );
// returns NaN

v = stdev( 1.0, -1.0 );
// returns NaN
```

</section>

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<section class="notes">

</section>

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<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var stdev = require( '@stdlib/stats/base/dists/beta/stdev' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + EPS;
    v = stdev( alpha, beta );
    console.log( 'α: %d, β: %d, SD(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</section>

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<section class="references">

</section>

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<section class="links">

[beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution

[stdev]: https://en.wikipedia.org/wiki/Standard_deviation

</section>

<!-- /.links -->
