 igappf
 Dataplot Vol 2 Auxiliary Chapter

# IGAPPF

Name:
IGAPPF (LET)
Type:
Library Function
Purpose:
Compute the the inverted gamma percent point function.
Description:
The standard form of the generalized gamma distribution has the following cumulative disribution function: where is the complete gamma function and is the incomplete gamma function.

The percent point function is the inverse of the cumulative distribution function. The cumulative distribution sums the probability from 0 to the given x value (i.e., the integral of the above function). The percent point function takes a cumulative probability value and computes the corresponding x value.

The inverted gamma is the special case where the second shape parameter, c, is equal to -1.

Syntax:
LET <y> = IGAPPF(<p>,<k>,<loc>, <scale>)             <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or a variable in the range 0 to 1;
<y> is a variable or a parameter (depending on what <p> is) where the computed inverted gamma ppf value is saved;
<k> is a positive number, parameter, or variable that specifies the first shape parameter;
<loc> is a number, parameter, or variable that defines the location parameter;
<scale> is a number, parameter, or variable that defines the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

Examples:
LET A = IGAPPF(0.95,1.5)
LET Y = IGAPPF(X,1.5)
LET Y = IGAPPF(X,1.5,10,2)
PLOT IGAPPF(P,1.5,10,2) FOR P = 0.01 0.01 0.99
Default:
None
Synonyms:
None
Related Commands:
 IGACDF = Compute the inverted gamma cumulative distribution function. IGAPDF = Compute the inverted gamma probability density function. GGDCDF = Compute the generalized gamma cumulative distribution function. GGDPDF = Compute the generalized gamma probability density function. GGDPPF = Compute the generalized gamma percent point function. GAMCDF = Compute the gamma cumulative distribution function. GAMPDF = Compute the gamma probability density function. GAMPPF = Compute the gamma percent point function. WEICDF = Compute the Weibull cumulative distribution function. WEIPDF = Compute the Weibull probability density function. WEIPPF = Compute the Weibull percent point function. EXPCDF = Compute the exponential cumulative distribution function. EXPPDF = Compute the exponential probability density function. EXPPPF = Compute the exponential percent point function. CHSCDF = Compute the chi-square cumulative distribution function. CHSPDF = Compute the chi-square probability density function. CHSPPF = Compute the chi-square percent point function.
Reference:
"Continuous Univariate Distributions", 2nd. ed., Johnson, Kotz, and Balakrishnan, John Wiley and Sons, 1994 (chapter 17).

"Statistical Distributions", 2nd. Edition, Evans, Hastings, and Peacock, Wiley and Sons, 1993 (chapter 18).

Applications:
Reliability
Implementation Date:
1998/5
Program:
LET G = DATA 1 2 5 10
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE AUTOMATIC
LOOP FOR K = 1 1 4
LET G1 = G(K)
X1LABEL GAMMA = ^G1
PLOT IGAPPF(P,G1) FOR P = 0.05 0.01 0.95
END OF LOOP
END OF MULTIPLOT

Date created: 6/5/2001
Last updated: 4/4/2003