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Dataplot Vol 2 Vol 1

GAMHAZ

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

      h(x) = GAMPDF(x,gamma)/(1 - GAMCDF(x,gamma)) x, gamma > 0

    where gamma is the shape parameter and GAMPDF and GAMCDF are the probability density and cumulative distribution functions of the gamma distribution respectively.

Syntax:
    LET <y> = GAMHAZ(<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 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 = GAMCDF(3,1.5)
    LET X2 = GAMCDF(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.
    GAMCHAZ = Compute the gamma cumulative 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 Hazard Function (Gamma = 1) 
    PLOT GAMHAZ(X,1) FOR X = 0.1 0.1 5.5 
    TITLE Gamma Hazard Function (Gamma = 0.5) 
    PLOT GAMHAZ(X,0.5) FOR X = 0.1 0.1 5.5 
    TITLE Gamma Hazard Function (Gamma = 2) 
    PLOT GAMHAZ(X,2) FOR X = 0.1 0.1 5.5 
    TITLE Gamma Hazard Function (Gamma = 5) 
    PLOT GAMHAZ(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
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