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Dataplot Vol 2 Vol 1


    Library Function
    Compute the Zipf cumulative distribution function.
    The Zipf distribution has the following probability mass function:

      p(x;alpha,n) = (1/x^alpha)/SUM[i=1 to n][1/i**alpha]
  x = 1, 2, ..., n; alpha > 1; n a positive integer

    with alpha and n denoting the shape parameters.

    Some sources parameterize this distribution with s = alpha - 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
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.
    Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 465-471.
    Distributional Modeling
Implementation Date:
    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
    plot generated by sample program

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