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Dataplot Vol 2 Vol 1

GLSPPF

Name:
    GLSPPF (LET)
Type:
    Library Function
Purpose:
    Compute the generalized logarithmic series percent point function.
Description:
    The generalized logarithmic series distribution has the following probability mass function:

      p(x;theta,beta) = (1/(beta*x))*(beta*x x)theta**x*(1-theta)**(beta*x-x)/ (-LOG(1-theta)) x = 1, 2, ...; 0 < theta < 1; 1 <= beta < -1/theta

    with theta and beta denoting the shape parameters.

    The cumulative distribution function is computed using the following recurrence relation given on pages 228-229 of Consul and Famoye:

      p(x+1;theta,beta) = (beta - x/(x+1))*theta*(1-theta)^(beta-1)* PROD[j=1 to x-1][(1+beta/(beta*x - j))*p(x;theta,beta)

    with

      p(1;theta,beta) = theta*(1-theta)**(beta-1)/(-LOG(1-theta))

      p(2;theta,beta) = (beta-(1/2))*theta*(1-theta)^(beta-1)*p(1;theta,beta)

    The percent point function is computed by summing the above recurence relation until the the specified probability is obtained.

Syntax:
    LET <y> = GLSPDF(<p>,<theta>,<beta>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a positive integer variable, number, or parameter in the range (0,1);
                <theta> is a number, parameter, or variable in the range (0,1) that specifies the first shape parameter;
                <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 generalized logarithmic series ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = GLSPPF(0.95,0.5,1.4)
    LET Y = GLSPPF(P,0.3,1.6)
    PLOT GLSPPF(P,0.3,1.6) FOR P = 0 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    GLSCDF = Compute the generalized logarithmic series cumulative distribution 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.
Reference:
    Consul and Famoye (2006), "Lagrangian Probability Distribution", Birkhauser, chapter 11.
Applications:
    Distributional Modeling
Implementation Date:
    2006/8
Program: 
     
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
x1label Probability
y1label X
.
xlimits 0 1
major xtic mark number 6
minor xtic mark number 3
.
multiplot 2 2
.
title Theta = 0.3, Beta = 1.8
plot glsppf(p,0.3,1.8) for p = 0  0.01  0.99
.
title Theta = 0.5, Beta = 1.5
plot glsppf(p,0.5,1.5) for p = 0  0.01  0.99
.
title Theta = 0.7, Beta = 1.2
plot glsppf(p,0.7,1.2) for p = 0  0.01  0.99
.
title Theta = 0.9, Beta = 1.1
plot glsppf(p,0.9,1.1) for p = 0  0.01  0.99
.
end of multiplot
.
justification center
move 50 97
text Percent Points for Generalized Logarithmic Series
    plot generated by sample program

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