 Dataplot Vol 2 Vol 1

# PAPCDF

Name:
PAPCDF (LET)
Type:
Library Function
Purpose:
Compute the Polya-Aeppli cumulative distribution function.
Description:
The formula for the Polya-Aeppli probability mass function is with and p denoting the shape parameters.

The cumulative distribution function is computed using the following recurrence relation (from page 379 of Johnson, Kemp, and Kotz) Syntax:
LET <y> = PAPCDF(<x>,<theta>,<p>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a non-negative integer variable, number, or parameter;
<theta> is a positive number or parameter that specifies the first shape parameter;
<p> is a positive number or parameter that specifies the second shape parameter;
<y> is a variable or a parameter where the computed Polya-Aeppli cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = PAPCDF(3,3,0.5)
LET Y = PAPCDF(X1,2,0.3)
PLOT PAPCDF(X,2,0.3) FOR X = 0 1 20
Default:
None
Synonyms:
None
Related Commands:
 PAPPDF = Compute the Polya-Aeppli probability mass function. PAPPPF = Compute the Polya-Aeppli percent point function. LPOPDF = 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. INTEGER FREQUENCY TABLE = Generate a frequency table at integer values with unequal bins. COMBINE FREQUENCY TABLE = Convert an equal width frequency table to an unequal width frequency table. KS PLOT = Generate a minimum chi-square plot. MAXIMUM LIKELIHOOD = Perform maximum likelihood estimation for a distribution.
References:
Douglas (1980), "Analysis with Standard Contagious Distributions", International Co-operative Publishing House, Fairland, MD.

Evans (1953), "Experimental Evidence Concerning Contagious Distributions in Ecology", Biometrika, 40, pp. 186-211.

Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 378-382.

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 Theta = 0.5, P = 0.5
plot papcdf(x,0.5,0.5) for x = 1 1 20
.
title Theta = 1, P = 0.5
plot papcdf(x,1,0.5) for x = 1 1 20
.
title Theta = 2.5, P = 0.5
plot papcdf(x,2.5,0.5) for x = 1 1 20
.
title Theta = 5, P = 0.5
plot papcdf(x,5,0.5) for x = 1 1 20
.
end of multiplot
.
justification center
move 50 97
text Cumulative Distribution for Polya-Aeppli
``` Date created: 6/20/2006
Last updated: 6/20/2006