EV2CHAZ

EV2CHAZ (LET)

Library Function

Compute the standard form of the extreme value type II (also known as the Frechet distribution) cumulative hazard function.

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

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

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

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.

LET A = EV2CHAZ(3,1.5)
LET X2 = EV2CHAZ(X1,GAMMA)

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.

None

None

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.

"Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994, (chapter 21).

Extreme Value Analysis

1998/4

    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