## @stdlib/stats-base-dists-rayleigh-pdf 0.1.0 • Public • Published

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# Probability Density Function

Rayleigh distribution probability density function (PDF).

The probability density function (PDF) for a Rayleigh random variable is

where `sigma > 0` is the scale parameter.

## Installation

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

## Usage

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

#### pdf( x, sigma )

Evaluates the probability density function for a Rayleigh distribution with scale parameter `sigma`.

```var y = pdf( 0.3, 1.0 );
// returns ~0.287

y = pdf( 2.0, 0.8 );
// returns ~0.137

y = pdf( -1.0, 0.5 );
// returns 0.0```

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

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

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

If provided `sigma < 0`, the function returns `NaN`.

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

If provided `sigma = 0`, the function evaluates the PDF of a degenerate distribution centered at `0`.

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

y = pdf( 0.0, 0.0 );
// returns Infinity

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

#### pdf.factory( sigma )

Returns a function for evaluating the probability density function (PDF) of a Rayleigh distribution with parameter `sigma` (scale parameter).

```var myPDF = pdf.factory( 4.0 );

var y = myPDF( 6.0 );
// returns ~0.122

y = myPDF( 4.0 );
// returns ~0.152```

## Examples

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

var sigma;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
sigma = randu() * 10.0;
y = pdf( x, sigma );
console.log( 'x: %d, σ: %d, f(x;σ): %d', x.toFixed( 4 ), sigma.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.

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