About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Probability Density Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Rayleigh][rayleigh-distribution] distribution probability density function (PDF).

The [probability density function][pdf] (PDF) for a [Rayleigh][rayleigh-distribution] random variable is

Probability density function (PDF) for a Rayleigh distribution.

where sigma > 0 is the scale parameter.

Installation

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

`Usage`

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

#### pdf( x, sigma )

Evaluates the [probability density function][pdf] for a [Rayleigh][rayleigh-distribution] distribution with scale parameter sigma.

`javascript 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.

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

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

If provided sigma < 0, the function returns NaN.

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

If provided sigma = 0, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at 0.

`javascript 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] (PDF) of a [Rayleigh][rayleigh-distribution] distribution with parameter sigma (scale parameter).

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

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

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

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var pdf = require( '@stdlib/stats-base-dists-rayleigh-pdf' );

var opts = { 'dtype': 'float64' }; var x = uniform( 10, 0.0, 10.0, opts ); var sigma = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, σ: %0.4f, f(x;σ): %0.4f', x, sigma, pdf );`

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/rayleigh/pdf.h"`

#### stdlib_base_dists_rayleigh_pdf( x, sigma )

Evaluates the probability density function (PDF) for a Rayleigh distribution.

`c double out = stdlib_base_dists_rayleigh_pdf( 0.3, 1.0 ); // returns ~0.287`

The function accepts the following arguments:

- x: [in] doubleinput value. - sigma:[in] double scale parameter.

`c double stdlib_base_dists_rayleigh_pdf( const double x, const double sigma );`

`$3`

`c #include "stdlib/stats/base/dists/rayleigh/pdf.h" #include #include

static double random_uniform( const double min, const double max ) { double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); return min + ( v*(max-min) ); }

int main( void ) { double sigma; double x; double y; int i;

for ( i = 0; i < 25; i++ ) { x = random_uniform( 0.0, 10.0 ); sigma = random_uniform( 0.0, 10.0 ); y = stdlib_base_dists_rayleigh_pdf( x, sigma ); printf( "x: %lf, σ: %lf, f(x;σ): %lf\n", x, sigma, y ); } }`

*

`Notice`

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

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-rayleigh-pdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-rayleigh-pdf

[test-image]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-rayleigh-pdf/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-rayleigh-pdf?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-rayleigh-pdf/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-rayleigh-pdf/main/LICENSE

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution


  
    About stdlib...
  

  We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

  The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

  When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`Probability Density Function`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Rayleigh][rayleigh-distribution] distribution probability density function (PDF).

The [probability density function][pdf] (PDF) for a [Rayleigh][rayleigh-distribution] random variable is

where sigma > 0 is the scale parameter.

`Installation`

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

`Usage`

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

#### pdf( x, sigma )

Evaluates the [probability density function][pdf] for a [Rayleigh][rayleigh-distribution] distribution with scale parameter sigma.

`javascript 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.

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

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

If provided sigma < 0, the function returns NaN.

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

If provided sigma = 0, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at 0.

`javascript 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] (PDF) of a [Rayleigh][rayleigh-distribution] distribution with parameter sigma (scale parameter).

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

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

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

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var pdf = require( '@stdlib/stats-base-dists-rayleigh-pdf' );

var opts = { 'dtype': 'float64' }; var x = uniform( 10, 0.0, 10.0, opts ); var sigma = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, σ: %0.4f, f(x;σ): %0.4f', x, sigma, pdf ); `

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/rayleigh/pdf.h" `

#### stdlib_base_dists_rayleigh_pdf( x, sigma )

Evaluates the probability density function (PDF) for a Rayleigh distribution.

`c double out = stdlib_base_dists_rayleigh_pdf( 0.3, 1.0 ); // returns ~0.287 `

The function accepts the following arguments:

- x: [in] double input value. - sigma: [in] double scale parameter.

`c double stdlib_base_dists_rayleigh_pdf( const double x, const double sigma ); `

`$3`

`c #include "stdlib/stats/base/dists/rayleigh/pdf.h" #include #include

static double random_uniform( const double min, const double max ) { double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); return min + ( v*(max-min) ); }

int main( void ) { double sigma; double x; double y; int i;

for ( i = 0; i < 25; i++ ) { x = random_uniform( 0.0, 10.0 ); sigma = random_uniform( 0.0, 10.0 ); y = stdlib_base_dists_rayleigh_pdf( x, sigma ); printf( "x: %lf, σ: %lf, f(x;σ): %lf\n", x, sigma, y ); } } `

*

`Notice`

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-rayleigh-pdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-rayleigh-pdf

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-rayleigh-pdf/main/LICENSE

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution