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Dataplot Vol 2 Vol 1


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

      p(x;theta,beta) = (1/(beta*x-1)*(beta*x-1  x)*theta**(x-1)*
(1-theta)**(beta*x-x)  x = 1, ...; 0 < theta < 1; 1 <= beta <= 1/theta

    with theta and beta denoting the shape parameters.

    The mean and variance of the Geeta distribution are:

      mu = (1-theta)/(1 - theta*beta)

      sigma2 = (beta-1)*theta*(1-theta)/(1-theta*beta)^3

    The Geeta distribution is sometimes parameterized in terms of its mean, mu, instead of theta. This results in the following probability mass function:

      p(x;mu,beta) = (1/(beta*x-1)*(beta*x-1  x)*
   x = 1, ...; mu >= 1; beta > 1

    For this parameterization, the variance is

      sigma2 = mu*(mu-1)*(beta*mu-1)/(beta-1)

    This probability mass function is also given in the form:

      p(x;mu,beta)=(beta*x-1  x)*((mu-1)/(beta*mu-mu))**(x-1)*

    Dataplot supports both parameterizations (see the Note section below).

    The cumulative distribution function is computed by summing the probability mass function.

    LET <y> = GETCDF(<x>,<shape>,<beta>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a positive integer variable, number, or parameter;
                <shape> is a number, parameter, or variable that specifies the valuie of theta (or mu);
                <beta> is a number, parameter, or variable that specifies the second shape parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed Geeta cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
    LET A = GETCDF(3,0.5,1.4)
    LET Y = GETCDF(X,0.3,1.6)
    PLOT GETCDF(X,0.3,1.6) FOR X = 1 1 20
    To use the MU parameterization, enter the command


    To restore the THETA parameterization, enter the command

Related Commands:
    GETPDF = Compute the Geeta probability mass function.
    GETPPF = Compute the Geeta percent point function.
    CONPDF = Compute the Consul probability mass function.
    GLSPDF = Compute the generalized logarithmic series probability mass function.
    DLGPDF = Compute the logarithmic series probability mass function.
    YULPDF = Compute the Yule probability mass function.
    ZETPDF = Compute the Zeta probability mass function.
    BGEPDF = Compute the beta geometric probability mass function.
    POIPDF = Compute the Poisson probability mass function.
    BINPDF = Compute the binomial probability mass function.
    Consul and Famoye (2006), "Lagrangian Probability Distribution", Birkhauser, chapter 8.

    Consul (1990), "Geeta Distribution and its Properties", Communications in Statistics--Theory and Methods, 19, pp. 3051-3068.

    Distributional Modeling
Implementation Date:
    set geeta definition theta
    title size 3
    tic label size 3
    label size 3
    legend size 3
    height 3
    x1label displacement 12
    y1label displacement 15
    multiplot corner coordinates 0 0 100 95
    multiplot scale factor 2
    label case asis
    title case asis
    case asis
    tic offset units screen
    tic offset 3 3
    title displacement 2
    y1label Probability
    x1label X
    ylimits 0 1
    major ytic mark number 6
    minor ytic mark number 3
    xlimits 0 20
    line blank
    spike on
    multiplot 2 2
    title Theta = 0.3, Beta = 1.8
    plot getcdf(x,0.3,1.8) for x = 1 1 20
    title Theta = 0.5, Beta = 1.5
    plot getcdf(x,0.5,1.5) for x = 1 1 20
    title Theta = 0.7, Beta = 1.2
    plot getcdf(x,0.7,1.2) for x = 1 1 20
    title Theta = 0.9, Beta = 1.1
    plot getcdf(x,0.9,1.1) for x = 1 1 20
    end of multiplot
    justification center
    move 50 97
    text Cumulative Distributions for Geeta Distribution
    plot generated by sample program

Date created: 8/23/2006
Last updated: 8/23/2006
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