 Dataplot Vol 2 Vol 1

# IGCDF

Name:
IGCDF (LET)
Type:
Library Function
Purpose:
Compute the inverse Gaussian cumulative distribution function with shape parameters and .
Description:
The inverse Gaussian distribution has the following cumulative distribution function: with and denoting the shape parameters and denoting the cumulative distribution function of the standard normal distribution.

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

Syntax:
LET <y> = IGCDF(<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 cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Note that the location and scale parameters are optional.

Examples:
LET A = IGCDF(3,2,1)
LET A = IGCDF(A1,2,1)
LET X2 = IGCDF(X1,2,3)
PLOT IGCDF(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:
 IGCHAZ = Compute the inverse Gaussian cumulative hazard function. IGHAZ = Compute the inverse Gaussian 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 Probability
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 IGCDF(X,2,1) FOR X = 0.01  0.01  5
TITLE GAMMA = 5, MU = 1
PLOT IGCDF(X,5,1) FOR X = 0.01  0.01  5
TITLE GAMMA = 2, MU = 2
PLOT IGCDF(X,2,2) FOR X = 0.01  0.01  5
TITLE GAMMA = 5, MU = 2
PLOT IGCDF(X,5,2) FOR X = 0.01  0.01  5
END OF MULTIPLOT
JUSTIFICATION CENTER
MOVE 50 97
CASE ASIS
TEXT Inverse Gaussian CDF
``` Date created: 7/7/2004
Last updated: 7/7/2004
Please email comments on this WWW page to alan.heckert@nist.gov.