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

Standard library statistical functions.

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# Mean

> [Inverse gamma][invgamma-distribution] distribution [expected value][expected-value].

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The [expected value][expected-value] for an [inverse-gamma][invgamma-distribution] random variable is

<!-- <equation class="equation" label="eq:invgamma_expectation" align="center" raw="\mathbb{E}\left[ X \right] = \frac{\beta}{\alpha-1}" alt="Expected value for an inverse-gamma distribution."> -->

<div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = \frac{\beta}{\alpha-1}" data-equation="eq:invgamma_expectation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/invgamma/mean/docs/img/equation_invgamma_expectation.svg" alt="Expected value for an inverse-gamma distribution.">
    <br>
</div>

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

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## Usage

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

#### mean( alpha, beta )

Returns the [expected value][expected-value] of an [inverse gamma][invgamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).

```javascript
var v = mean( 4.0, 12.0 );
// returns 4.0

v = mean( 8.0, 2.0 );
// returns ~0.286
```

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 `alpha <= 1`, the function returns `NaN`.

```javascript
var v = mean( 0.5, 1.0 );
// returns NaN

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

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

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

v = mean( 1.0, -1.0 );
// 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 EPS = require( '@stdlib/constants/float64/eps' );
var mean = require( '@stdlib/stats/base/dists/invgamma/mean' );

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 = mean( alpha, beta );
    console.log( 'α: %d, β: %d, E(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}
```

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</section>

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</section>

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[invgamma-distribution]: https://en.wikipedia.org/wiki/Inverse-gamma_distribution

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

</section>

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