Rayleigh Distribution

Parameters

Domain

Two-Parameter Rayleigh Distribution

Probability Density Function

Cumulative Distribution Function

One-Parameter Rayleigh Distribution

Probability Density Function

Cumulative Distribution Function

Worksheet and VBA Functions

The following worksheet and VBA functions are available for this distribution:

Description	VBA Functions	Worksheet Functions
Distribution Fitting	-	=DistFit("Rayleigh";Data;[Options]1)
Probability Density Function	RayleighPdf(x,sigma,[gamma])	=RayleighPdf(sigma;[gamma]) =DistPdf("Rayleigh(sigma;[gamma])";x)
Cumulative Distribution Function	RayleighCdf(x,sigma,[gamma])	=RayleighCdf(sigma;[gamma]) =DistCdf("Rayleigh(sigma;[gamma])";x)
Survival Function	RayleighSurv(x,sigma,[gamma])	=DistSurv("Rayleigh(sigma;[gamma])";x)
Hazard Function	RayleighHaz(x,sigma,[gamma])	=RayleighHaz(sigma;[gamma]) =DistHaz("Rayleigh(sigma;[gamma])";x)
Cumulative Hazard Function	RayleighCumHaz(x,sigma,[gamma])	=DistCumHaz("Rayleigh(sigma;[gamma])";x)
Inverse CDF (Quantile Function)	RayleighInv(P,sigma,[gamma])	=RayleighInv(sigma;[gamma]) =DistInv("Rayleigh(sigma;[gamma])";P)
Random Numbers	RayleighRand(sigma,[gamma])	=RayleighRand(sigma;[gamma]) =DistRand("Rayleigh(sigma;[gamma])")
Mode	RayleighMode(sigma,[gamma])	=DistMode("Rayleigh(sigma;[gamma])")
Mean	RayleighMean(sigma,[gamma])	=RayleighMean(sigma;[gamma]) =DistMean("Rayleigh(sigma;[gamma])")
Variance	RayleighVar(sigma,[gamma])	=RayleighVar(sigma;[gamma]) =DistVar("Rayleigh(sigma;[gamma])")
Standard Deviation	RayleighStdev(sigma,[gamma])	=RayleighStdev(sigma;[gamma]) =DistStdev("Rayleigh(sigma;[gamma])")
Skewness	RayleighSkew(sigma,[gamma])	=DistSkew("Rayleigh(sigma;[gamma])")
(Excess) Kurtosis	RayleighKurt(sigma,[gamma])	=DistKurt("Rayleigh(sigma;[gamma])")

1. The Options parameter is optional. Possible options: "gamma=value"  (example: "gamma=0")
2. The gamma parameter is optional (the default value is 0).