SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

GEPHAZ

Name:
    GEPHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the generalized Pareto hazard function with shape parameter gamma.
Description:
    The generalized Pareto distribution for the maximum order statistic has the following hazard function for non-negative gamma:

      h(x,gamma) = 1/(1 + gamma*x)    x > 0; gamma >= 0

    The generalized Pareto distribution for the maximum order statistic has the following hazard function for negative gamma:

      h(x,gamma) = 1/(1 + gamma*x)    x > = -1/gamma; gamma < 0
Syntax:
    LET <y> = GEPHAZ(<x>,<GAMMA>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable, number, or parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed generalized Pareto hazard value is stored;
                <GAMMA> is a positive number or parameter that specifies the shape parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = GEPHAZ(3,2)
    LET A = GEPHAZ(A1,4)
Note:
    The SET MINMAX command is used to specify whether the minimum order statistic or the maximumorder statistic form is used. Specifically, SET MINMAX 1 specifies the minimum order statistic while SET MINMAX 2 specifies the maximum order statistic. Currently, only the maximum order statistic form is supported, so it is not necessary to specify the SET MINMAX command.
Default:
    None
Synonyms:
    None
Related Commands:
    GEPCDF = Compute the generalized Pareto cumulative distribution function.
    GEPPDF = Compute the generalized Pareto probability density function.
    GEPPPF = Compute the generalized Pareto percent point function.
    GEPCHAZ = Compute the generalized Pareto cumulative hazard function.
    CHSPDF = Compute the chi-square probability density function.
    NORPDF = Compute the normal probability density function.
    WEIPDF = Compute the Weibull probability density function.
    EV1PDF = Compute the Gumbel (EV1) probability density function.
    EV2PDF = Compute the Gumbel (EV1) probability density function.
Reference:
    "Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994.
Applications:
    Reliability, Extreme Value Analysis
Implementation Date:
    1998/4
Program:
        MULTIPLOT 2 2 
        MULTIPLOT CORNER COORDINATES 5 5 95 95 
        TITLE CASE ASIS 
        TITLE Generalized Pareto Hazard Function (Gamma = 1) 
        PLOT GEPHAZ(X,1) FOR X = 0.01 0.01 5
        TITLE Generalized Pareto Hazard Function (Gamma = 2) 
        PLOT GEPHAZ(X,2) FOR X = 0.01 0.01 5
        TITLE Generalized Pareto Hazard Function (Gamma = 5) 
        PLOT GEPHAZ(X,5) FOR X = 0.01 0.01 5
        TITLE Generalized Pareto Hazard Function (Gamma = 0.5) 
        PLOT GEPHAZ(X,0.5) FOR X = 0.01 0.01 5 
        END OF MULTIPLOT 
        
    plot generated by sample program

Date created: 10/9/2001
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.