The Rayleigh Distribution

The Rayleigh distribution can be used to model the velocity of particles whose velocity in the x and y directions are independent and follow a normal distribution.

The Rayleigh distribution has a scale parameter. The probability density function is:

The Rayleigh distribution is a special case of the The Weibull Distribution.

The Rayleigh distribution is implemented by the RayleighDistribution class. It has one constructor that takes the scale parameter as its only argument.

The following constructs the Rayleigh distribution with scale parameter 1.8:

var rayleigh = new RayleighDistribution(1.8);

Dim rayleigh = New RayleighDistribution(1.8)

let rayleigh = RayleighDistribution(1.8)

The RayleighDistribution class has two specific properties, LocationParameter and ScaleParameter, which return the location parameter (smallest possible value) and scale parameter of the distribution.

RayleighDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator. The second and third parameters are the location and scale parameters of the distribution.

var random = new MersenneTwister();
double sample = RayleighDistribution.Sample(random, 1.8);

Dim random = New MersenneTwister()
Dim sample = RayleighDistribution.Sample(random, 1.8)

let random = MersenneTwister()
let sample = RayleighDistribution.Sample(random, 1.8)

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..