 Dataplot Vol 2 Vol 1

# IGHAZ

Name:
IGHAZ (LET)
Type:
Library Function
Purpose:
Compute the inverse Gaussian hazard function with shape parameters and .
Description:
The inverse Gaussian distribution has the following hazard function: with and denoting the shape parameters and IGCDF and IGPDF denoting the cumulative distribution function and probability density function, respectively, of the inverse Gaussian distribution.

The inverse Gaussian distribution can be generalized with location and scale parameters in the usual way.

Syntax:
LET <y> = IGHAZ(<x>,<gamma>,<mu>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable or a parameter;
<gamma> is number or parameter that specifies the first shape parameter;
<mu> is number or parameter that specifies the second shape parameter;
<loc> is number or parameter that specifies the location parameter;
<scale> is number or parameter that specifies the scale parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed inverse Gaussian hazard value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Note that the location and scale parameters are optional.

Examples:
LET A = IGHAZ(3,2,1)
LET A = IGHAZ(A1,2,1)
LET X2 = IGHAZ(X1,2,3)
PLOT IGHAZ(X,2,1.5) FOR X = 0.1 0.1 5
Note:
The case where = 1 is referred to as the Wald distribution. Enter HELP WALPDF for details.
Default:
None
Synonyms:
None
Related Commands:
 IGCDF = Compute the inverse Gaussian cumulative distribution function. IGCHAZ = Compute the inverse Gaussian cumulative hazard function. IGPDF = Compute the inverse Gaussian probability density function. IGPPF = Compute the inverse Gaussian percent point function. CHSPDF = Compute the chi-square probability density function. FPDF = Compute the F probability density function. NORPDF = Compute the normal probability density function. TPDF = Compute the t probability density function. WEIPDF = Compute the Weibull probability density function. WALPDF = Compute the Wald probability density function. FLPDF = Compute the fatigue life probability density function. RIGPDF = Compute the reciprocal inverse Gaussian probability density function.
Reference:
"Continuous Univariate Distributions--Volume 1", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15.

"Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley, 2000, pp. 114-116.

Applications:
Distributional Modeling
Implementation Date:
1990/5: Original implementation
2003/12: Modified to treat as a shape parameter instead of a location parameter.
Program:
```
Y1LABEL Hazard
X1LABEL X
LABEL CASE ASIS
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 12
MULTIPLOT SCALE FACTOR 2
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
TITLE GAMMA = 2, MU = 1
PLOT IGHAZ(X,2,1) FOR X = 0.01  0.01  5
TITLE GAMMA = 5, MU = 1
PLOT IGHAZ(X,5,1) FOR X = 0.01  0.01  5
TITLE GAMMA = 2, MU = 2
PLOT IGHAZ(X,2,2) FOR X = 0.01  0.01  5
TITLE GAMMA = 5, MU = 2
PLOT IGHAZ(X,5,2) FOR X = 0.01  0.01  5
END OF MULTIPLOT
JUSTIFICATION CENTER
MOVE 50 97
CASE ASIS
TEXT Inverse Gaussian Hazard
``` Date created: 7/7/2004
Last updated: 7/7/2004