# Rayleigh > Rayleigh distribution.
## Usage ```javascript var rayleigh = require( '@stdlib/stats/base/dists/rayleigh' ); ``` #### rayleigh Rayleigh distribution. ```javascript var dist = rayleigh; // returns {...} ``` The namespace contains the following distribution functions:
- [`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.
The namespace contains the following functions for calculating distribution properties:
- [`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. - [`variance( sigma )`][@stdlib/stats/base/dists/rayleigh/variance]: Rayleigh distribution variance.
The namespace contains a constructor function for creating a [Rayleigh][rayleigh-distribution] distribution object.
- [`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 ~0.185 ```
## Examples ```javascript var objectKeys = require( '@stdlib/utils/keys' ); var rayleigh = require( '@stdlib/stats/base/dists/rayleigh' ); console.log( objectKeys( rayleigh ) ); ```