Dataplot Vol 2 Vol 1

# EV2HAZ

Name:
EV2HAZ (LET)
Type:
Library Function
Purpose:
Compute the standard form of the extreme value type II (also known as the Frechet distribution) hazard function.
Description:
For the minimum order statistic, the standard form of the hazard function is:

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

where is a positive number that is the shape parameter, EV2PDF is the probability density of the EV2 distribution, and EV2CDF is the cumulative distribution of the EV2 distribution.

Syntax:
LET <y> = EV2HAZ(<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 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 = EV2HAZ(3,1.5)
LET X2 = EV2HAZ(X1,GAMMA)
Note:
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.
Default:
None
Synonyms:
None
Related Commands:
 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.
Reference:
"Continuous Univariate Distributions: Volume 1", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994, (chapter 21).
Applications:
Extreme Value Analysis, Reliability Analysis
Implementation Date:
1998/4
Program:
```    SET MINMAX 2
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 5 5 95 95
TITLE CASE ASIS
TITLE PLOT EV2 Hazard Function (Gamma = 1)
PLOT EV2HAZ(X,1) FOR X = 0.01 0.01 5.5
TITLE PLOT EV2 Hazard Function (Gamma = 0.5)
PLOT EV2HAZ(X,0.5) FOR X = 0.01 0.01 5.5
TITLE PLOT EV2 Hazard Function (Gamma = 2)
PLOT EV2HAZ(X,2) FOR X = 0.01 0.01 5.5
TITLE PLOT EV2 Hazard Function (Gamma = 5)
PLOT EV2HAZ(X,5) FOR X = 0.01 0.01 5.5
END OF PLOT
```

Date created: 10/9/2001
Last updated: 4/4/2003