Dataplot Vol 2 Vol 1

# GLSPPF

Name:
GLSPPF (LET)
Type:
Library Function
Purpose:
Compute the generalized logarithmic series percent point function.
Description:
The generalized logarithmic series distribution has the following probability mass function:

with and denoting the shape parameters.

The cumulative distribution function is computed using the following recurrence relation given on pages 228-229 of Consul and Famoye:

with

The percent point function is computed by summing the above recurence relation until the the specified probability is obtained.

Syntax:
LET <y> = GLSPDF(<p>,<theta>,<beta>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a positive integer variable, number, or parameter in the range (0,1);
<theta> is a number, parameter, or variable in the range (0,1) that specifies the first shape parameter;
<beta> is a number, parameter, or variable that specifies the second shape parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed generalized logarithmic series ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = GLSPPF(0.95,0.5,1.4)
LET Y = GLSPPF(P,0.3,1.6)
PLOT GLSPPF(P,0.3,1.6) FOR P = 0 0.01 0.99
Default:
None
Synonyms:
None
Related Commands:
 GLSCDF = Compute the generalized logarithmic series cumulative distribution 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 11.
Applications:
Distributional Modeling
Implementation Date:
2006/8
Program:
```
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 glsppf(p,0.3,1.8) for p = 0  0.01  0.99
.
title Theta = 0.5, Beta = 1.5
plot glsppf(p,0.5,1.5) for p = 0  0.01  0.99
.
title Theta = 0.7, Beta = 1.2
plot glsppf(p,0.7,1.2) for p = 0  0.01  0.99
.
title Theta = 0.9, Beta = 1.1
plot glsppf(p,0.9,1.1) for p = 0  0.01  0.99
.
end of multiplot
.
justification center
move 50 97
text Percent Points for Generalized Logarithmic Series
```

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