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Dataplot Vol 2 Vol 1

LOSPPF

Name:
    LOSPPF (LET)
Type:
    Library Function
Purpose:
    Compute the lost games percent point function.
Description:
    The formula for the lost games probability mass function is

      p(x;p,r) = (2*x-r x)*(1-p)**(x-r)*(p)^x*(r/(2*x-r)) X = R, R+ 1, ...; 0.5 < p < 1

    with p and r denoting the shape parameters. The r parameter is restricted to non-negative integers.

    The cumulative distribution function 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 function until the specified probability is reached.

Syntax:
    LET <y> = LOSPPF(<p>,<p>,<r>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a variable, number, or parameter in the interval (0,1);
                <p> is a number or parameter in the range (0.5,1) that specifies the first shape parameter;
                <r> is a number or parameter denoting a positive integer that specifies the second shape parameter;
                <y> is a variable or a parameter where the computed lost games ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = LOSPPF(0.95,0.7,3)
    LET Y = LOSPPF(P1,0.7,2)
    PLOT LOSPPF(P,0.6,5) FOR P = 0 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    LOSCDF = Compute the lost games cumulative distribution function.
    LOSPDF = Compute the lost games probability mass function.
    BTAPDF = Compute the Borel-Tanner 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:
    Luc Devroye (1986), "Non-Uniform Random Variate Generation", Springer-Verlang, pp. 758-759.

    Kemp and Kemp (1968), "On a Distribution Associated with Certain Stochastic Processes", Journal of the Royal Statistical Society, Series B, 30, pp. 401-410.

    Haight (1961), "A Distribution Analogous to the Borel-Tanner Distribution", Biometrika, 48, pp. 167-173.

    Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 445-447.

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
x1label Probability
y1label X
.
xlimits 0 1
major xtic mark number 6
minor xtic mark number 3
.
multiplot 2 2
.
title P = 0.6, R = 3
plot losppf(p,0.6,3) for p = 0  0.01  0.99
.
title P = 0.7, R = 3
plot losppf(p,0.7,3) for p = 0  0.01  0.99
.
title P = 0.8, R = 3
plot losppf(p,0.8,3) for p = 0  0.01  0.99
.
title P = 0.9, R = 3
plot losppf(p,0.9,3) for p = 0  0.01  0.99
.
end of multiplot
.
justification center
move 50 97
text Percent Point for Lost Games
    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.