Dataplot Vol 2 Vol 1

# GETPPF

Name:
GETPPF (LET)
Type:
Library Function
Purpose:
Compute the Geeta percent point function.
Description:
The Geeta distribution has the following probability mass function:

with and denoting the shape parameters.

The mean and variance of the Geeta distribution are:

=

2 =

The Geeta distribution is sometimes parameterized in terms of its mean, , instead of . This results in the following probability mass function:

For this parameterization, the variance is

2 =

This probability mass function is also given in the form:

Dataplot supports both parameterizations (see the Note section below).

The cumulative distribution function is computed by summing the probability mass function. The percent point function is computed by summing the cumulative distribution function until the appropriate probability is reached.

Syntax:
LET <y> = GETPPF(<p>,<shape>,<beta>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a positive integer variable, number, or parameter in the interval (0,1);
<shape> is a number, parameter, or variable that specifies the valuie of theta (or mu);
<beta> is a number, parameter, or variable that specifies the second shape parameter;
<y> is a variable or a parameter (depending on what <p> is) where the computed Geeta ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = GETPPF(0.95,0.5,1.4)
LET Y = GETPPF(P,0.3,1.6)
PLOT GETPPF(P,0.3,1.6) FOR P = 0 0.01 0.99
Note:
To use the MU parameterization, enter the command

SET GEETA DEFINITION MU

To restore the THETA parameterization, enter the command

SET GEETA DEFINITION THETA
Default:
None
Synonyms:
None
Related Commands:
 GETCDF = Compute the Geeta cumulative distribution function. GETPDF = Compute the Geeta probability mass function. CONPDF = Compute the Consul probability mass function. GLSPDF = Compute the generalized logarithmic series probability mass function. DLGPDF = Compute the logarithmic series probability mass function. YULPDF = Compute the Yule probability mass function. ZETPDF = Compute the Zeta probability mass function. BGEPDF = Compute the beta geometric probability mass function. POIPDF = Compute the Poisson probability mass function. BINPDF = Compute the binomial probability mass function.
Reference:
Consul and Famoye (2006), "Lagrangian Probability Distribution", Birkhauser, chapter 8.

Consul (1990), "Geeta Distribution and its Properties", Communications in Statistics--Theory and Methods, 19, pp. 3051-3068.

Applications:
Distributional Modeling
Implementation Date:
2006/8
Program:
```
set geeta definition theta
title size 3
tic label size 3
label size 3
legend size 3
height 3
x1label displacement 12
y1label displacement 15
.
multiplot corner coordinates 0 0 100 95
multiplot scale factor 2
label case asis
title case asis
case asis
tic offset units screen
tic offset 3 3
title displacement 2
x1label Probability
y1label X
.
xlimits 0 1
major xtic mark number 6
minor xtic mark number 3
.
multiplot 2 2
.
title Theta = 0.3, Beta = 1.8
plot getppf(p,0.3,1.8) for p = 0  0.01  0.99
.
title Theta = 0.5, Beta = 1.5
plot getppf(p,0.5,1.5) for p = 0  0.01  0.99
.
title Theta = 0.7, Beta = 1.2
plot getppf(p,0.7,1.2) for p = 0  0.01  0.99
.
title Theta = 0.9, Beta = 1.1
plot getppf(p,0.9,1.1) for p = 0  0.01  0.99
.
end of multiplot
.
justification center
move 50 97
text Percent Point Functions for Geeta Distribution
```

Date created: 8/23/2006
Last updated: 8/23/2006