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

0.2.2 • Public • Published

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# Probability Density Function

Fréchet distribution probability density function.

The probability density function for a Fréchet random variable is

where `alpha > 0` is the shape, `s > 0` the scale and `m` the location parameter.

## Installation

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

## Usage

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

#### pdf( x, alpha, s, m )

Evaluates the probability density function (PDF) for a Fréchet distribution with shape `alpha`, scale `s`, and location `m` at a value `x`.

```var y = pdf( 10.0, 2.0, 3.0, 5.0 );
// returns ~0.1

y = pdf( -3.0, 1.0, 2.0, -4.0 );
// returns ~0.271

y = pdf( 0.0, 2.0, 1.0, -1.0 );
// returns ~0.736```

If provided `x <= m`, the function returns `0`.

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

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

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

y = pdf( 0.0, NaN, 1.0, 0.0 );
// returns NaN

y = pdf( 0.0, 1.0, NaN, 0.0);
// returns NaN

y = pdf( 0.0, 1.0, 1.0, NaN );
// returns NaN```

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

```var y = pdf( 2.0, -0.1, 1.0, 1.0 );
// returns NaN

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

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

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

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

#### pdf.factory( alpha, s, m )

Returns a function for evaluating the probability density function of a Fréchet distribution with shape `alpha`, scale `s`, and location `m`.

```var mypdf = pdf.factory( 3.0, 3.0, 5.0 );

var y = mypdf( 10.0 );
// returns ~0.104

y = mypdf( 7.0 );
// returns ~0.173```

## Examples

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

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

for ( i = 0; i < 100; i++ ) {
alpha = randu() * 10.0;
x = randu() * 10.0;
s = randu() * 10.0;
m = randu() * 10.0;
y = pdf( x, alpha, s, m );
console.log( 'x: %d, α: %d, s: %d, m: %d, f(x;α,s,m): %d', x.toFixed( 4 ), 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-pdf`

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