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

EV2CHAZ

Name:
    EV2CHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the standard form of the extreme value type II (also known as the Frechet distribution) cumulative hazard function.
Description:
    For the minimum order statistic, the standard form of the cumulative hazard function is:

      H(x) = (-x)**(-gamma)        x <= 0, gamma > 0

    For the maximum order statistic, the standard form of the cumulative hazard function is:

      H(x) = -DLOG[1 - EV2CDF(x,gamma)]      x >= 0, gamma > 0

    where gamma is a positive number that is the shape parameter and EV2CDF is the cumulative distribution of the EV2 distribution.

Syntax:
    LET <y> = EV2CHAZ(<x>,<gamma>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable, a number, or a parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed extreme value type II cumulative hazard value is saved;
                <gamma> is a number or parameter that specifies the shape parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = EV2CHAZ(3,1.5)
    LET X2 = EV2CHAZ(X1,GAMMA)
Note:
    The SET MINMAX command specifies whether the minimum or maximum order statistic form is used. Entering SET MINMAX 2 specifies the maximum order statistic while SET MINMAX 1 specifies the minimum order statistic. This command is required before using the EV1CDF function.
Default:
    None
Synonyms:
    None
Related Commands:
    EV2CDF = Compute the extreme value type II cumulative distribution function.
    EV2PDF = Compute the extreme value type II probability density function.
    EV2HAZ = Compute the extreme value type II hazard function.
    EV1PDF = Compute the extreme value type I probability density function.
    WEIPDF = Compute the Weibull probability density function.
    EXPPDF = Compute the exponential probability density function.
Reference:
    "Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994, (chapter 21).
Applications:
    Extreme Value Analysis
Implementation Date:
    1998/4
Program:
        SET MINMAX 2 
        MULTIPLOT 2 2 
        MULTIPLOT CORNER COORDINATES 5 5 95 95 
        TITLE CASE ASIS 
        TITLE PLOT EV2 Cumulative Hazard Function (Gamma = 1) 
        PLOT EV2CHAZ(X,1) FOR X = 0.01 0.01 5.5 
        TITLE PLOT EV2 Cumulative Hazard Function (Gamma = 0.5) 
        PLOT EV2CHAZ(X,0.5) FOR X = 0.01 0.01 5.5 
        TITLE PLOT EV2 Cumulative Hazard Function (Gamma = 2) 
        PLOT EV2CHAZ(X,2) FOR X = 0.01 0.01 5.5 
        TITLE PLOT EV2 Cumulative Hazard Function (Gamma = 5) 
        PLOT EV2CHAZ(X,5) FOR X = 0.01 0.01 5.5 
        END OF PLOT 
        
    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.