LPOCDF

LPOCDF (LET)

Library Function

Compute the Lagrange-Poisson cumulative distribution function.

The Lagrange Poisson distribution has probability mass function

with and denoting the shape parameters.

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

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.

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

None

None

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.

Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 394-400.

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

Distributional Modeling

2006/6

 
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title Lambda = 0.3, Theta = 1
plot lpocdf(x,0.3,1) for x = 1 1 20
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title Lambda = 0.5, Theta = 1
plot lpocdf(x,0.5,1) for x = 1 1 20
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title Lambda = 0.7, Theta = 1
plot lpocdf(x,0.7,1) for x = 1 1 20
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title Lambda = 0.9, Theta = 1
plot lpocdf(x,0.9,1) for x = 1 1 20
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text Cumulative Distribution for Lagrange-Poisson