GAMCHAZ

GAMCHAZ (LET)

Library Function

Compute the standard form of the gamma cumulative hazard function.

The standard form of the gamma distribution has the following cumulative hazard function:

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

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.

LET A = GAMCHAZ(3,1.5)
LET X2 = GAMCHAZ(X1,GAMMA)

If is 1, this distribution reduces to the exponential distribution. If is an integer, then this distribution is also known as an Erlang distribution.

None

None

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.

"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).

Reliability

1998/4

    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