Dataplot Vol 2 Vol 1

# RAYCDF

Name:
RAYCDF (LET)
Type:
Library Function
Purpose:
Compute the Rayleigh cumulative distribution function.
Description:
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.

Syntax:
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.
Examples:
LET Y = RAYCDF(3)
LET Y = RAYCDF(X1,0,SIGMA)
PLOT RAYCDF(X,0,SIGMA) FOR X = 0.01 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 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.
Reference:
"Continuous Univariate Distributions: Volume I", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 453, 686.
Applications:
Distributional Modeling, Statistical Physics
Implementation Date:
6/2004
Program:
```
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
TITLE CASE ASIS
TITLE Rayleigh Cumulative Disribution
PLOT RAYCDF(X) FOR X = 0  0.01  5
```

Date created: 7/7/2004
Last updated: 7/7/2004