Dataplot Vol 2 Vol 1

LPOCDF

Name:
LPOCDF (LET)
Type:
Library Function
Purpose:
Compute the Lagrange-Poisson cumulative distribution function.
Description:
The Lagrange Poisson distribution has probability mass function

with and denoting the shape parameters.

The cumulative distribution function is computed by summing the probability mass function.

Syntax:
LET <y> = LPOCDF(<x>,<lambda>,<theta>)>
<SUBSET/EXCEPT/FOR qualification>
where <x> is a positive integer variable, number, or parameter;
<lambda> is a number or parameter in the range (0,1) that specifies the first shape parameter;
<theta> is a positive number or parameter that specifies the second shape parameter;
<y> is a variable or a parameter where the computed Lagrange-Poisson cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = LPOCDF(3,0.5,3)
LET Y = LPOCDF(X1,0.3,2)
PLOT LPOCDF(X,0.3,2) FOR X = 0 1 20
Default:
None
Synonyms:
None
Related Commands:
 LPOPDF = Compute the Lagrange-Poisson probability mass function. LPOPPF = Compute the Lagrange-Poisson percent point function. BTAPDF = Compute the Borel-Tanner probability mass function. LOSPDF = Compute the lost games probability mass function. POIPDF = Compute the Poisson probability mass function. HERPDF = Compute the Hermite probability mass function. BINPDF = Compute the binomial probability mass function. NBPDF = Compute the negative binomial probability mass function. GEOPDF = Compute the geometric probability mass function.
Reference:
Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 394-400.

P. C. Consul (1989), "Generalized Poisson Distributions", Dekker, New York.

Applications:
Distributional Modeling
Implementation Date:
2006/6
Program:
```
title size 3
tic label size 3
label size 3
legend size 3
height 3
multiplot scale factor 1.5
x1label displacement 12
y1label displacement 17
.
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 Lambda = 0.3, Theta = 1
plot lpocdf(x,0.3,1) for x = 1 1 20
.
title Lambda = 0.5, Theta = 1
plot lpocdf(x,0.5,1) for x = 1 1 20
.
title Lambda = 0.7, Theta = 1
plot lpocdf(x,0.7,1) for x = 1 1 20
.
title Lambda = 0.9, Theta = 1
plot lpocdf(x,0.9,1) for x = 1 1 20
.
end of multiplot
.
justification center
move 50 97
text Cumulative Distribution for Lagrange-Poisson
```

Date created: 6/20/2006
Last updated: 6/20/2006