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Dataplot Vol 2 Vol 1

IGACHAZ

Name:
    IGACHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the standard form of the inverted gamma cumulative hazard function.
Description:
    The standard form of the inverted gamma cumulative hazard function is:

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

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

    The inverted gamma is a special case of the generalized gamma distribution where the second shape parameter is equal to -1.

Syntax:
    LET <y> = IGACHAZ(<x>,<gamma>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a positive number, parameter, or a variable;
                <y> is a variable or a parameter (depending on what <x> is) where the computed inverted gamma cumulative hazard value is saved;
                <gamma> is a positive number, parameter, or variable that specifies the shape parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = IGACHAZ(3,1.5)
    LET Y = IGACHAZ(X,1.5)
    PLOT IGACHAZ(X,1.5) FOR X = 5 0.1 15
Default:
    None
Synonyms:
    None
Related Commands:
    IGACDF = Compute the inverted gamma cumulative distribution function.
    IGAPDF = Compute the inverted gamma probability density function.
    IGAPPF = Compute the inverted gamma percent point function.
    GGDPDF = Compute the generalized gamma probability density function.
    GAMPDF = Compute the gamma probability density function.
    WEIPDF = Compute the Weibull probability density function.
    EXPPDF = Compute the exponential probability density function.
    CHSPDF = Compute the chi-square probability density function.
Reference:
    "Continuous Univariate Distributions", 2nd. ed., Johnson, Kotz, and Balakrishnan, John Wiley and Sons, 1994 (chapter 17).

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

Applications:
    Reliability
Implementation Date:
    1998/5
Program:
        LET G = DATA 0.5 1 2 5 
        . 
        MULTIPLOT 2 2 
        MULTIPLOT CORNER COORDINATES 0 0 100 100 
        TITLE AUTOMATIC 
        LOOP FOR K = 1 1 4 
           LET G1 = G(K) 
           X1LABEL GAMMA = ^G1 
           PLOT IGACHAZ(X,G1) FOR X = 0.1 0.1 10 
        END OF LOOP 
        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.