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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
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