EV2HAZ
Name:
Type:
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:
Synonyms:
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:
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
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alan.heckert@nist.gov.
