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Dataplot Vol 2 Vol 1

LPOCDF

Name:
    LPOCDF (LET)
Type:
    Library Function
Purpose:
    Compute the Lagrange-Poisson cumulative distribution function.
Description:
    The Lagrange Poisson distribution has probability mass function

      p(x;lambda,theta) = theta*(theta+x*lambda)**(x-1)*
EXP(-theta-x*lambda)/x!    x = 0, 1, ...; 0 < ;lambda < 1; theta > 0

    with theta and lambda denoting the shape parameters.

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

Syntax:
    LET <y> = LPOCDF(<x>,<lambda>,<theta>)>
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a positive integer variable, number, or parameter;
                <lambda> is a number or parameter in the range (0,1) that specifies the first shape parameter;
                <theta> is a positive number or parameter that specifies the second shape parameter;
                <y> is a variable or a parameter where the computed Lagrange-Poisson cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = LPOCDF(3,0.5,3)
    LET Y = LPOCDF(X1,0.3,2)
    PLOT LPOCDF(X,0.3,2) FOR X = 0 1 20
Default:
    None
Synonyms:
    None
Related Commands:
    LPOPDF = Compute the Lagrange-Poisson probability mass function.
    LPOPPF = Compute the Lagrange-Poisson percent point function.
    BTAPDF = Compute the Borel-Tanner probability mass function.
    LOSPDF = Compute the lost games probability mass function.
    POIPDF = Compute the Poisson probability mass function.
    HERPDF = Compute the Hermite probability mass function.
    BINPDF = Compute the binomial probability mass function.
    NBPDF = Compute the negative binomial probability mass function.
    GEOPDF = Compute the geometric probability mass function.
Reference:
    Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 394-400.

    P. C. Consul (1989), "Generalized Poisson Distributions", Dekker, New York.

Applications:
    Distributional Modeling
Implementation Date:
    2006/6
Program:
     
    title size 3
    tic label size 3
    label size 3
    legend size 3
    height 3
    multiplot scale factor 1.5
    x1label displacement 12
    y1label displacement 17
    .
    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 Lambda = 0.3, Theta = 1
    plot lpocdf(x,0.3,1) for x = 1 1 20
    .
    title Lambda = 0.5, Theta = 1
    plot lpocdf(x,0.5,1) for x = 1 1 20
    .
    title Lambda = 0.7, Theta = 1
    plot lpocdf(x,0.7,1) for x = 1 1 20
    .
    title Lambda = 0.9, Theta = 1
    plot lpocdf(x,0.9,1) for x = 1 1 20
    .
    end of multiplot
    .
    justification center
    move 50 97
    text Cumulative Distribution for Lagrange-Poisson
        
    plot generated by sample program

Date created: 6/20/2006
Last updated: 6/20/2006
Please email comments on this WWW page to alan.heckert@nist.gov.