Dataplot Vol 2 Vol 1

ZETCDF

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

with denoting the shape parameter and denoting the Riemann zeta function

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> = ZETCDF(<x>,<alpha>)
<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 shape parameter;
<y> is a variable or a parameter where the computed zeta cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = ZETCDF(3,1.5)
LET Y = ZETCDF(X1,2.3)
PLOT ZETCDF(X,2.3) FOR X = 1 1 50
Default:
None
Synonyms:
None
Related Commands:
 ZETPDF = Compute the Zeta probability mass function. ZETPPF = Compute the Zeta percent point function. ZIPPDF = Compute the Zipf cumulative distribution 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.

Devroye (1986), "Non-Uniform Random Variate Generation", Springer-Verlang, New York.

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 alpha = 1.5
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
.
let alpha = 2.0
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
.
let alpha = 2.5
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
.
let alpha = 3.0
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
.
end of multiplot
.
justification center
move 50 97
text Zeta Cumulative Distribution Functions
```

Date created: 6/5/2006
Last updated: 6/5/2006