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Dataplot Vol 2 Vol 1


    Library Function
    Compute the Zipf percent point 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. The percent point function is the inverse of the cumulative distribution function and is obtained by computing the cumulative distribution until the specified probability is obtained.

    LET <y> = ZIPPPF(<p>,<alpha>,<n>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a variable, number, or parameter in the range (0,1);
                <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 ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
    LET A = ZIPPPF(0.95,1.5,100)
    LET Y = ZIPPPF(X1,2.3,1000)
    PLOT ZIPPPF(X,2.3,100) FOR X = 1 1 100
Related Commands:
    ZIPCDF = Compute the Zipf cumulative distribution function.
    ZIPPDF = Compute the Zipf probability mass 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
    x1label Probability
    xlimits 0 1
    major xtic mark number 6
    minor xtic mark number 3
    y1label X
    line blank
    spike on
    multiplot 2 2
    let n = 100
    let alpha = 1.5
    title Alpha = ^alpha
    plot zipppf(p,alpha,n) for p = 0  0.01  1
    let alpha = 2.0
    title Alpha = ^alpha
    plot zipppf(p,alpha,n) for p = 0  0.01  1
    let alpha = 2.5
    title Alpha = ^alpha
    plot zipppf(p,alpha,n) for p = 0  0.01  1
    let alpha = 3.0
    title Alpha = ^alpha
    plot zipppf(p,alpha,n) for p = 0  0.01  1
    end of multiplot
    justification center
    move 50 97
    text Zipf Percent Point Functions
    plot generated by sample program

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