Rayleigh distribution.
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Rayleigh distribution.
bash
npm install @stdlib/stats-base-dists-rayleighscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var rayleigh = require( '@stdlib/stats-base-dists-rayleigh' );javascript
var dist = rayleigh;
// returns {...}cdf( x, sigma )][@stdlib/stats/base/dists/rayleigh/cdf]: Rayleigh distribution cumulative distribution function.logcdf( x, sigma )][@stdlib/stats/base/dists/rayleigh/logcdf]: Rayleigh distribution logarithm of cumulative distribution function.logpdf( x, sigma )][@stdlib/stats/base/dists/rayleigh/logpdf]: Rayleigh distribution logarithm of probability density function (PDF).mgf( t, sigma )][@stdlib/stats/base/dists/rayleigh/mgf]: Rayleigh distribution moment-generating function (MGF).pdf( x, sigma )][@stdlib/stats/base/dists/rayleigh/pdf]: Rayleigh distribution probability density function (PDF).quantile( p, sigma )][@stdlib/stats/base/dists/rayleigh/quantile]: Rayleigh distribution quantile function.entropy( sigma )][@stdlib/stats/base/dists/rayleigh/entropy]: Rayleigh distribution differential entropy.kurtosis( sigma )][@stdlib/stats/base/dists/rayleigh/kurtosis]: Rayleigh distribution excess kurtosis.mean( sigma )][@stdlib/stats/base/dists/rayleigh/mean]: Rayleigh distribution expected value.median( sigma )][@stdlib/stats/base/dists/rayleigh/median]: Rayleigh distribution median.mode( sigma )][@stdlib/stats/base/dists/rayleigh/mode]: Rayleigh distribution mode.skewness( sigma )][@stdlib/stats/base/dists/rayleigh/skewness]: Rayleigh distribution skewness.stdev( sigma )][@stdlib/stats/base/dists/rayleigh/stdev]: Rayleigh distribution standard deviation.variance( sigma )][@stdlib/stats/base/dists/rayleigh/variance]: Rayleigh distribution variance.Rayleigh( [sigma] )][@stdlib/stats/base/dists/rayleigh/ctor]: Rayleigh distribution constructor.javascript
var Rayleigh = require( '@stdlib/stats-base-dists-rayleigh' ).Rayleigh;
var dist = new Rayleigh( 2.0 );
var y = dist.pdf( 0.8 );
// returns ~0.185javascript
var rayleigh = require( '@stdlib/stats-base-dists-rayleigh' );
/*
* The Rayleigh distribution can be used to model wind speeds.
* Let's consider a scenario where we want to estimate various properties related to wind speeds.
*/
// Set the Rayleigh distribution parameter (scale parameter):
var s = 10.0;
// Calculate mean, variance, and standard deviation of the Rayleigh distribution:
console.log( rayleigh.mean( s ) );
// => ~12.533
console.log( rayleigh.variance( s ) );
// => ~42.920
console.log( rayleigh.stdev( s ) );
// => ~6.551
// Evaluate the Probability Density Function (PDF) for a specific wind speed:
var w = 15.0;
console.log( rayleigh.pdf( w, s ) );
// => ~0.049
// Determine Cumulative Distribution Function (CDF) for wind speeds up to a certain value:
var t = 15.0;
console.log( rayleigh.cdf( t, s ) );
// => ~0.675
// Calculate the probability of wind speeds exceeding the threshold:
var p = 1.0 - rayleigh.cdf( t, s );
console.log( 'Probability of wind speeds exceeding ' + t + ' m/s:', p );
// Find the wind speed at which there's a 70% chance it won't exceed using the Quantile function:
var c = 0.7;
console.log( rayleigh.quantile( c, s ) );
// => ~15.518
