Rayleigh

Rayleigh distribution.

Usage

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

rayleigh

Rayleigh distribution.

var dist = rayleigh;
// returns {...}

The namespace contains the following distribution functions:

cdf( x, sigma ): Rayleigh distribution cumulative distribution function.
logcdf( x, sigma ): Rayleigh distribution logarithm of cumulative distribution function.
logpdf( x, sigma ): Rayleigh distribution logarithm of probability density function (PDF).
mgf( t, sigma ): Rayleigh distribution moment-generating function (MGF).
pdf( x, sigma ): Rayleigh distribution probability density function (PDF).
quantile( p, sigma ): Rayleigh distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

entropy( sigma ): Rayleigh distribution differential entropy.
kurtosis( sigma ): Rayleigh distribution excess kurtosis.
mean( sigma ): Rayleigh distribution expected value.
median( sigma ): Rayleigh distribution median.
mode( sigma ): Rayleigh distribution mode.
skewness( sigma ): Rayleigh distribution skewness.
stdev( sigma ): Rayleigh distribution standard deviation.
variance( sigma ): Rayleigh distribution variance.

The namespace contains a constructor function for creating a Rayleigh distribution object.

Rayleigh( [sigma] ): Rayleigh distribution constructor.

var Rayleigh = require( '@stdlib/stats/base/dists/rayleigh' ).Rayleigh;

var dist = new Rayleigh( 2.0 );

var y = dist.pdf( 0.8 );
// returns ~0.185

Examples

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