ZETCDF

ZETCDF (LET)

Library Function

Compute the Zeta cumulative distribution function.

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.

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.

LET A = ZETCDF(3,1.5)
LET Y = ZETCDF(X1,2.3)
PLOT ZETCDF(X,2.3) FOR X = 1 1 50

None

None

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.

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.

Distributional Modeling

2006/5

 
multiplot corner coordinates 0 0 100 95
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title case asis
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tic offset 3 3
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y1label Probability
ylimits 0 1
major ytic mark number 6
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x1label X
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spike on
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multiplot 2 2
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let alpha = 1.5
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
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let alpha = 2.0
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
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let alpha = 2.5
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
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let alpha = 3.0
title Alpha = ^alpha
plot zetcdf(x,alpha) for x = 1 1 20
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end of multiplot
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move 50 97
text Zeta Cumulative Distribution Functions