Rayleigh

Rayleigh distribution constructor.

Usage

var Rayleigh = require( '@stdlib/math/base/dists/rayleigh/ctor' );

Rayleigh( [sigma] )

Returns an Rayleigh distribution object.

var rayleigh = new Rayleigh();

var mu = rayleigh.mean;
// returns ~1.253

By default, sigma = 1.0. To create a distribution having a different scale parameter sigma, provide a parameter value.

var rayleigh = new Rayleigh( 4.0 );

var mu = rayleigh.mean;
// returns ~5.013

rayleigh

A Rayleigh distribution object has the following properties and methods...

Writable Properties

rayleigh.sigma

Scale parameter of the distribution. sigma must be a positive number.

var rayleigh = new Rayleigh( 2.0 );

var sigma = rayleigh.sigma;
// returns 2.0

rayleigh.sigma = 3.0;

sigma = rayleigh.sigma;
// returns 3.0

Computed Properties

Rayleigh.prototype.entropy

Returns the differential entropy.

var rayleigh = new Rayleigh( 4.0 );

var entropy = rayleigh.entropy;
// returns ~2.328

Rayleigh.prototype.kurtosis

Returns the excess kurtosis.

var rayleigh = new Rayleigh( 4.0 );

var kurtosis = rayleigh.kurtosis;
// returns ~0.245

Rayleigh.prototype.mean

Returns the median.

var rayleigh = new Rayleigh( 4.0 );

var mu = rayleigh.mean;
// returns ~5.013

Rayleigh.prototype.median

Returns the median.

var rayleigh = new Rayleigh( 4.0 );

var median = rayleigh.median;
// returns ~4.71

Rayleigh.prototype.mode

Returns the mode.

var rayleigh = new Rayleigh( 4.0 );

var mode = rayleigh.mode;
// returns 4.0

Rayleigh.prototype.skewness

Returns the skewness.

var rayleigh = new Rayleigh( 4.0 );

var skewness = rayleigh.skewness;
// returns ~0.631

Rayleigh.prototype.stdev

Returns the standard deviation.

var rayleigh = new Rayleigh( 4.0 );

var s = rayleigh.stdev;
// returns ~2.62

Rayleigh.prototype.variance

Returns the variance.

var rayleigh = new Rayleigh( 4.0 );

var s2 = rayleigh.variance;
// returns ~6.867

Methods

Rayleigh.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.cdf( 1.5 );
// returns ~0.245

Rayleigh.prototype.logcdf( x )

Evaluates the natural logarithm of the cumulative distribution function (CDF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.logcdf( 1.5 );
// returns ~-1.406

Rayleigh.prototype.logpdf( x )

Evaluates the natural logarithm of the probability density function (PDF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.logpdf( 0.8 );
// returns ~-1.689

Rayleigh.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.mgf( 0.5 );
// returns ~5.586

Rayleigh.prototype.pdf( x )

Evaluates the probability density function (PDF).

var rayleigh = new Rayleigh( 2.0 );

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

Rayleigh.prototype.quantile( p )

Evaluates the quantile function at probability p.

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.quantile( 0.5 );
// returns ~2.355

y = quantile( 1.9 );
// returns NaN

Examples

var Rayleigh = require( '@stdlib/math/base/dists/rayleigh/ctor' );

var rayleigh = new Rayleigh( 2.0, 4.0 );

var mu = rayleigh.mean;
// returns ~2.507

var mode = rayleigh.mode;
// returns 2.0

var s2 = rayleigh.variance;
// returns ~1.717

var y = rayleigh.cdf( 0.8 );
// returns ~0.077