# @stdlib/stats-base-dists-frechet-mean

0.2.2 • Public • Published

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# Mean

Fréchet distribution expected value.

The expected value for a Fréchet random variable shape `α > 0`, scale `s > 0`, and location parameter `m` is

where `Γ` is the gamma function.

## Installation

`npm install @stdlib/stats-base-dists-frechet-mean`

## Usage

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

#### mean( alpha, s, m )

Returns the expected value for a Fréchet distribution with shape `alpha > 0`, scale `s > 0`, and location parameter `m`.

```var y = mean( 2.0, 1.0, 1.0 );
// returns ~2.772

y = mean( 4.0, 4.0, -1.0 );
// returns ~3.902

y = mean( 1.0, 1.0, 2.0 );
// returns Infinity```

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

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

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

y = mean( 1.0, 1.0, NaN );
// returns NaN```

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

```var y = mean( 0.0, 3.0, 2.0 );
// returns NaN

y = mean( 0.0, -1.0, 2.0 );
// returns NaN```

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

```var y = mean( 1.0, 0.0, 2.0 );
// returns NaN

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

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var mean = require( '@stdlib/stats-base-dists-frechet-mean' );

var alpha;
var m;
var s;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*20.0 ) + EPS;
s = ( randu()*20.0 ) + EPS;
m = ( randu()*20.0 ) - 40.0;
y = mean( alpha, s, m );
console.log( 'α: %d, s: %d, m: %d, E(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}```

## Notice

This package is part of 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, see the main project repository.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-frechet-mean`

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