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Dataplot Vol 2 Vol 1

LOSCDF

Name:
    LOSCDF (LET)
Type:
    Library Function
Purpose:
    Compute the lost games cumulative distribution 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.

Syntax:
    LET <y> = LOSCDF(<x>,<p>,<r>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a positive integer variable, number, or parameter;
                <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 cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = LOSCDF(3,0.7,3)
    LET Y = LOSCDF(X1,0.7,2)
    PLOT LOSCDF(X,0.6,5) FOR X = 5 1 50
Default:
    None
Synonyms:
    None
Related Commands:
    LOSPDF = Compute the lost games probability mass function.
    LOSPPF = Compute the lost games percent point 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
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 P = 0.6, R = 3
plot loscdf(x,0.6,3) for x = 1 1 20
.
title P = 0.7, R = 3
plot loscdf(x,0.7,3) for x = 1 1 20
.
title P = 0.8, R = 3
plot loscdf(x,0.8,3) for x = 1 1 20
.
title P = 0.9, R = 3
plot loscdf(x,0.9,3) for x = 1 1 20
.
end of multiplot
.
justification center
move 50 97
text Cumulative Distribution 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.