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Rayleigh distribution probability density function (PDF).
The probability density function (PDF) for a Rayleigh random variable is
where sigma > 0
is the scale parameter.
To use in Observable,
pdf = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-rayleigh-pdf@umd/browser.js' )
To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:
var pdf = require( 'path/to/vendor/umd/stats-base-dists-rayleigh-pdf/index.js' )
To include the bundle in a webpage,
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-rayleigh-pdf@umd/browser.js"></script>
If no recognized module system is present, access bundle contents via the global scope:
<script type="text/javascript">
(function () {
window.pdf;
})();
</script>
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
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
<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-rayleigh-pdf@umd/browser.js"></script>
<script type="text/javascript">
(function () {
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 ) );
}
})();
</script>
</body>
</html>
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.
See LICENSE.
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