RAYCDF

RAYCDF (LET)

Library Function

Compute the Rayleigh cumulative distribution function.

The Rayleigh distribution is a special case of the distribution with degrees of freedom parameter = 2 and scale parameter . It is also a special case of the Weibull distribution with shape parameter = 2 and scale parameter = . Note that some sources may define the Rayleigh distribution as a Weibull with shape parameter = 2 and scale parameter = .

The Rayleigh distribution has the following cumulative disribution function:

with and denoting the location and scale parameters, respectively.

The standard Rayleigh distribution is the case with = 0 and = 1.

LET <y> = RAYCDF(<x>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable or a parameter;
            <loc> is an optional number or parameter that specifies the value of the location parameter;
            <scale> is an optional positive number or parameter that specifies the value of the scale parameter;
            <y> is a variable or a parameter (depending on what <x> is) where the computed Rayleigh cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET Y = RAYCDF(3)
LET Y = RAYCDF(X1,0,SIGMA)
PLOT RAYCDF(X,0,SIGMA) FOR X = 0.01 0.01 5

None

None

RAYPDF	= Compute the Rayleigh probability density function.
RAYPPF	= Compute the Rayleigh percent point function.
MAXPDF	= Compute the Maxwell probability density function.
CHPDF	= Compute the chi probability density function.
WEIPDF	= Compute the Weibull probability density function.
NORPDF	= Compute the normal probability density function.
LGNPDF	= Compute the lognormal probability density function.

"Continuous Univariate Distributions: Volume I", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 453, 686.

Distributional Modeling, Statistical Physics

6/2004

 
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
TITLE CASE ASIS
TITLE Rayleigh Cumulative Disribution
PLOT RAYCDF(X) FOR X = 0  0.01  5