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Dataplot Vol 2 Vol 1

GAMCHAZ

Name:
    GAMCHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the standard form of the gamma cumulative hazard function.
Description:
    The standard form of the gamma distribution has the following cumulative hazard function:

      H(x) = -LOG[1 - GAMCDF(x,gamma)]     x, gamma > 0

    where gamma is the shape parameter and GAMCDF is the cumulative distribution functions of the gamma distribution.

Syntax:
    LET <y> = GAMCHAZ(<x>,<gamma>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a positive number, a number, or a variable;
                <y> is a variable or a parameter (depending on what <x> is) where the computed gamma 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 = GAMCHAZ(3,1.5)
    LET X2 = GAMCHAZ(X1,GAMMA)
Note:
    If gamma is 1, this distribution reduces to the exponential distribution. If gamma is an integer, then this distribution is also known as an Erlang distribution.
Default:
    None
Synonyms:
    None
Related Commands:
    GAMCDF = Compute the gamma cumulative distribution function.
    GAMPDF = Compute the gamma probability density function.
    GAMPPF = Compute the gamma percent point function.
    GAMHAZ = Compute the gamma hazard function.
    WEIPDF = Compute the Weibull probability density function.
    EXPPDF = Compute the exponential probability density function.
    CHSPDF = Compute the chi-square probability density function.
    IGAPDF = Compute the inverted gamma probability density function.
    GGDPDF = Compute the generalized gamma probability density function.
Reference:
    "Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994 (chapter 17).

    "Statistical Distributions", 2nd. Edition, Evans, Hastings, and Peacock, Wiley and Sons, 1993 (chapter 18).

Applications:
    Reliability
Implementation Date:
    1998/4
Program:
        MULTIPLOT CORNER COORDINATES 5 5 95 95 
        MULTIPLOT 2 2 
        TITLE CASE ASIS 
        TITLE Gamma Cumulative Hazard (Gamma = 1) 
        PLOT GAMCHAZ(X,1) FOR X = 0.1 0.1 5.5 
        TITLE Gamma Cumulative Hazard (Gamma = 0.5) 
        PLOT GAMCHAZ(X,0.5) FOR X = 0.1 0.1 5.5 
        TITLE Gamma Cumulative Hazard (Gamma = 2) 
        PLOT GAMCHAZ(X,2) FOR X = 0.1 0.1 5.5 
        TITLE Gamma Cumulative Hazard (Gamma = 5) 
        PLOT GAMCHAZ(X,5) FOR X = 0.1 0.1 10 
        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.