@stdlib/stats/base/dists/kumaraswamy/mean/README.md

Standard library statistical functions.

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# Mean

> [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution [expected value][mean].

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The [mean][mean] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable is

<!-- <equation class="equation" label="eq:kumaraswamy_mean" align="center" raw="\mathbb{E} \left[ X \right] = {b\Gamma(1+{\tfrac {1}{a}})\Gamma(b)}{\Gamma(1+{\tfrac{1}{a}}+b)}" alt="Mean for a Kumaraswamy's double bounded distribution."> -->

<div class="equation" align="center" data-raw-text="\mathbb{E} \left[ X \right] = {b\Gamma(1+{\tfrac {1}{a}})\Gamma(b)}{\Gamma(1+{\tfrac{1}{a}}+b)}" data-equation="eq:kumaraswamy_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/mean/docs/img/equation_kumaraswamy_mean.svg" alt="Mean for a Kumaraswamy's double bounded distribution.">
    <br>
</div>

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where `a` is the first shape parameter, `b` the second shape parameter, and `Γ` denotes the [gamma function][gamma-function].

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## Usage

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

#### mean( a, b )

Returns the [expected value][mean] of a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with first shape parameter `a` and second shape parameter `b`.

```javascript
var v = mean( 1.5, 1.5 );
// returns ~0.512

v = mean( 4.0, 12.0 );
// returns ~0.481

v = mean( 2.0, 8.0 );
// returns ~0.3
```

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

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

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

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

```javascript
var y = mean( -1.0, 2.0 );
// returns NaN

y = mean( 0.0, 2.0 );
// returns NaN
```

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

```javascript
var y = mean( 2.0, -1.0 );
// returns NaN

y = mean( 2.0, 0.0 );
// returns NaN
```

</section>

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</section>

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## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var mean = require( '@stdlib/stats/base/dists/kumaraswamy/mean' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randu() * 10.0;
    b = randu() * 10.0;
    v = mean( a, b );
    console.log( 'a: %d, b: %d, E(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}
```

</section>

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</section>

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</section>

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[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function

[kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution

[mean]: https://en.wikipedia.org/wiki/Mean

</section>

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