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Dataplot Vol 2 Vol 1

RAYPPF

Name:
    RAYPPF (LET)
Type:
    Library Function
Purpose:
    Compute the Rayleigh percent point function.
Description:
    The Rayleigh distribution is a special case of the chi distribution with degrees of freedom parameter = 2 and scale parameter sigma. It is also a special case of the Weibull distribution with shape parameter = 2 and scale parameter = SQRT(2)*sigma. Note that some sources may define the Rayleigh distribution as a Weibull with shape parameter = 2 and scale parameter = sigma.

    The Rayleigh distribution has the following percent point function:

      G(x,u,sigma) = u + sigma*SQRT(2*LOG(1/(1-P)))
 0 <= p < 1; sigma > 0

    with mu and sigma denoting the location and scale parameters, respectively.

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

Syntax:
    LET <y> = RAYPPF(<p>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a variable,number, or a parameter in the interval [0,1);
                <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 ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET Y = RAYPPF(0.95)
    LET Y = RAYPPF(P1,0,SIGMA)
    PLOT RAYPPF(P,0,SIGMA) FOR P = 0 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    RAYCDF = Compute the Rayleigh cumulative distribution function.
    RAYPDF = Compute the Rayleigh probability density function.
    MAXPDF = Compute the Maxwell cumulative distribution 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
Implementation Date:
    6/2004
Program:
     
    X1LABEL Probability
    Y1LABEL X
    TITLE Rayleigh Percent Point
    LABEL CASE ASIS
    TITLE CASE ASIS
    PLOT RAYPPF(P) FOR P = 0  0.01  0.99
        
    plot generated by sample program

Date created: 7/7/2004
Last updated: 7/7/2004
Please email comments on this WWW page to alan.heckert@nist.gov.