Dataplot Vol 2 Vol 1

# ZIPCDF

Name:
ZIPCDF (LET)
Type:
Library Function
Purpose:
Compute the Zipf cumulative distribution function.
Description:
The Zipf distribution has the following probability mass function:

with and n denoting the shape parameters.

Some sources parameterize this distribution with s = - 1 (so that the distribution is defined for s > 0).

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

Syntax:
LET <y> = ZIPCDF(<x>,<alpha>,<n>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a positive integer variable, number, or parameter;
<alpha> is a number or parameter greater than 1 that specifies the first shape parameter;
<n> is a number or parameter that is a positive integer that specifies the second shape parameter;
<y> is a variable or a parameter where the computed Zipf cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = ZIPCDF(3,1.5,100)
LET Y = ZIPCDF(X1,2.3,1000)
PLOT ZIPCDF(X,2.3,100) FOR X = 1 1 100
Default:
None
Synonyms:
None
Related Commands:
 ZIPPDF = Compute the Zipf probability mass function. ZIPPPF = Compute the Zipf percent point function. ZETPDF = Compute the Zeta probability mass function. YULPDF = Compute the Yule probability mass function. BGEPDF = Compute the beta-geometric (Waring) probability mass function. BTAPDF = Compute the Borel-Tanner probability mass function. DLGPDF = Compute the logarithmic series probability mass function.
Reference:
Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 465-471.
Applications:
Distributional Modeling
Implementation Date:
2006/5
Program:
```
multiplot corner coordinates 0 0 100 95
multiplot scale factor 2
case asis
label case asis
title case asis
tic offset units screen
tic offset 3 3
title displacement 2
y1label displacement 17
x1label displacement 12
.
y1label Probability
ylimits 0 1
major ytic mark number 6
minor ytic mark number 3
x1label X
line blank
spike on
.
multiplot 2 2
let n = 100
.
let alpha = 1.5
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
.
let alpha = 2.0
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
.
let alpha = 2.5
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
.
let alpha = 3.0
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
.
end of multiplot
.
justification center
move 50 97
text Zipf Cumulative Distribution Functions
```

Date created: 6/5/2006
Last updated: 6/5/2006
Please email comments on this WWW page to alan.heckert@nist.gov.