 Dataplot Vol 2 Vol 1

# CONCDF

Name:
CONCDF (LET)
Type:
Library Function
Purpose:
Compute the Consul probability mass function.
Description:
The Consul distribution has the following probability mass function: with and m denoting the shape parameters. The case where m = 1 reduces to the geometric distribution. For this reason, the Consul distribution is also referred to as the generalized geometric distribution.

The mean and variance of the Consul distribution are:  2 = The Consul distribution is also parameterized in terms of its mean, , which results in the following probability mass function:  can be expressed in terms of : For this parameterization, the mean and variance are:  2 = Dataplot supports both parameterizations (see the Note section below).

Dataplot computes the cumulative distribution function using the following recurrence relation given on page 320 of Consul and Famoye: where . If the parameterization is used, it is converted to the parameterization and the above recurrence relation is applied.

Syntax:
LET <y> = CONCDF(<x>,<shape>,<m>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a positive integer variable, number, or parameter;
<shape> is a number, parameter, or variable that specifies the valuie of theta (or mu);
<m> 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 Consul cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = CONCDF(3,0.5,1.4)
LET Y = CONCDF(X,0.3,1.6)
PLOT CONCDF(X,0.3,1.6) FOR X = 1 1 20
Note:
To use the MU parameterization, enter the command

SET CONSUL DEFINITION MU

To restore the THETA parameterization, enter the command

SET CONSUL DEFINITION THETA
Default:
None
Synonyms:
None
Related Commands:
 CONCDF = Compute the Consul cumulative distribution function. CONPDF = Compute the Consul probability mass function. GEOPDF = Compute the geometric probability mass function. GETPDF = Compute the Geeta 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.

Famoye (1997), "Generalized Geometric and Some of its Applications", Journal of Mathematical Sciences, 8, pp. 1-13.

Consul (1990), "New Class of Location-Parameter Discrete Probability Distributions and Their Chaacterizations", Communications in Statistics--Theory and Methods, 19, pp. 4653-4666.

Applications:
Distributional Modeling
Implementation Date:
2006/8
Program:
```
set consul 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
y1label Probability
x1label X
.
ylimits 0 1
major ytic mark number 6
minor ytic mark number 3
xlimits 0 20
line blank
spike on
.
multiplot 2 2
.
title Theta = 0.3, M = 1.8
plot concdf(x,0.3,1.8) for x = 1 1 20
.
title Theta = 0.5, M = 1.5
plot concdf(x,0.5,1.5) for x = 1 1 20
.
title Theta = 0.7, M = 1.2
plot concdf(x,0.7,1.2) for x = 1 1 20
.
title Theta = 0.9, M = 1.1
plot concdf(x,0.9,1.1) for x = 1 1 20
.
end of multiplot
.
justification center
move 50 97
text Cumulative Distribution Functions for Consul
``` Date created: 8/23/2006
Last updated: 8/23/2006