ZIPCDF

ZIPCDF (LET)

Library Function

Compute the Zipf cumulative distribution function.

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.

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.

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

None

None

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.

Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 465-471.

Distributional Modeling

2006/5

 
multiplot corner coordinates 0 0 100 95
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tic offset 3 3
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y1label Probability
ylimits 0 1
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x1label X
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multiplot 2 2
let n = 100
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let alpha = 1.5
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
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let alpha = 2.0
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
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let alpha = 2.5
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
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let alpha = 3.0
title Alpha = ^alpha
plot zipcdf(x,alpha,n) for x = 1 1 100
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end of multiplot
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text Zipf Cumulative Distribution Functions