Cdf.Rayleigh Method

CdfRayleigh Method

Evaluates the Rayleigh cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double Rayleigh(
	double x,
	double alpha
)

Public Shared Function Rayleigh ( 
	x As Double,
	alpha As Double
) As Double

public:
static double Rayleigh(
	double x, 
	double alpha
)

static member Rayleigh : 
        x : float * 
        alpha : float -> float

x: Type: SystemDouble
A double scalar value representing the argument at which the function is to be evaluated. It must be non-negative.
alpha: Type: SystemDouble
A double scalar value representing the scale parameter.

Type: Double
A double scalar value representing the probability that a Rayleigh random variable takes a value less than or equal to x.

Remarks

Method Cdf.Rayleigh is a special case of Weibull distribution function where the shape parameter gamma is 2.0; that is,

$F(x)=1-e^{-\frac{x^2}{2\alpha^2}}$

where alpha is the scale parameter.

Plot of Rayleigh Distribution Function