SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1


    Library Function
    Compute the Polya-Aeppli percent point function.
    The formula for the Polya-Aeppli probability mass function is

      p(x;theta,p) = EXP(-theta)        x = 0;
 = EXP(-theta)*p**x*SUM[j=1 to x][(x-1  j-1)*(theta*(1-p)/p)**j/j!]
 x = 1, ...; 0 < p < 1; theta > 0

    with theta and p denoting the shape parameters.

    The cumulative distribution function is computed using the following recurrence relation (from page 379 of Johnson, Kemp, and Kotz)

      p(x+1;theta,p) = (theta*(1-p)/(x+1))*SUM[j=0 TO x][(x+1-j)*p**(x-j)*

    The percent point function is computed by computing the cumulative distribution function until the appropriate probability is obtained.

    LET <y> = PAPPPF(<x>,<theta>,<p>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable, number, or parameter in the interval (0,1);
                <theta> is a positive number or parameter that specifies the first shape parameter;
                <p> is a positive number or parameter that specifies the second shape parameter;
                <y> is a variable or a parameter where the computed Polya-Aeppli ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
    LET A = PAPPPF(0.95,3,0.5)
    LET Y = PAPPPF(P,2,0.3)
    PLOT PAPPPF(P,2,0.3) FOR P = 0 0.01 0.99
Related Commands:
    PAPCDF = Compute the Polya-Aeppli cumulative distribution function.
    PAPPDF = Compute the Polya-Aeppli probability mass function.
    LPOPDF = 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.
    INTEGER FREQUENCY TABLE = Generate a frequency table at integer values with unequal bins.
    COMBINE FREQUENCY TABLE = Convert an equal width frequency table to an unequal width frequency table.
    KS PLOT = Generate a minimum chi-square plot.
    MAXIMUM LIKELIHOOD = Perform maximum likelihood estimation for a distribution.
    Douglas (1980), "Analysis with Standard Contagious Distributions", International Co-operative Publishing House, Fairland, MD.

    Evans (1953), "Experimental Evidence Concerning Contagious Distributions in Ecology", Biometrika, 40, pp. 186-211.

    Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 378-382.

    Distributional Modeling
Implementation Date:
    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
    x1label Probability
    y1label X
    xlimits 0 1
    major xtic mark number 6
    minor xtic mark number 3
    multiplot 2 2
    title Theta = 0.5, P = 0.5
    plot papcdf(x,0.5,0.5) for x = 0  0.01  0.99
    title Theta = 1, P = 0.5
    plot papcdf(x,1,0.5) for x = 0  0.01  0.99
    title Theta = 2.5, P = 0.5
    plot papcdf(x,2.5,0.5) for x = 0  0.01  0.99
    title Theta = 5, P = 0.5
    plot papcdf(x,5,0.5) for x = 0  0.01  0.99
    end of multiplot
    justification center
    move 50 97
    text Percent Point for Polya-Aeppli
    plot generated by sample program

Date created: 6/20/2006
Last updated: 6/20/2006
Please email comments on this WWW page to