The Truncated Generalized Poisson Distribution and its Estimation

P. C. Consul; Felix Famoye

doi:10.1080/03610928908830114

The Truncated Generalized Poisson Distribution and its Estimation

P. C. Consul, Felix Famoye

Statistics, Actuarial & Data Sciences

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

A discrete probability model always gets truncated during the sampling process and the point of truncation depends upon the sample size. Also, the generalized Poisson distribution cannot be used with full justification when the second parameter is negative. To avoid these problems a truncated generalized Poisson distribution is defined and studied. Estimation of its parameters by moments method, maximum likelihood method and a mixed method are considered. Some examples are given to illustrate the effect on the parameters’ estimates when a non-truncated GPD is used instead of a truncated GPD.

Original language	English
Pages (from-to)	3635-3648
Number of pages	14
Journal	Communications in Statistics - Theory and Methods
Volume	18
Issue number	10
DOIs	https://doi.org/10.1080/03610928908830114
State	Published - Jan 1989

Keywords

Lagrange expansion
Truncated generalized Poisson distribution
estimation
maximum likelihood
ratio of frequencies

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10.1080/03610928908830114

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title = "The Truncated Generalized Poisson Distribution and its Estimation",

abstract = "A discrete probability model always gets truncated during the sampling process and the point of truncation depends upon the sample size. Also, the generalized Poisson distribution cannot be used with full justification when the second parameter is negative. To avoid these problems a truncated generalized Poisson distribution is defined and studied. Estimation of its parameters by moments method, maximum likelihood method and a mixed method are considered. Some examples are given to illustrate the effect on the parameters{\textquoteright} estimates when a non-truncated GPD is used instead of a truncated GPD.",

keywords = "Lagrange expansion, Truncated generalized Poisson distribution, estimation, maximum likelihood, ratio of frequencies",

author = "Consul, {P. C.} and Felix Famoye",

note = "Funding Information: The authors express their gratefulness to Professor Edward J. Dudewicz for suggesting this problem and for reading the first draft of this work. Also, this work was financially supported by the NSERC of Canada.",

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AU - Famoye, Felix

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N2 - A discrete probability model always gets truncated during the sampling process and the point of truncation depends upon the sample size. Also, the generalized Poisson distribution cannot be used with full justification when the second parameter is negative. To avoid these problems a truncated generalized Poisson distribution is defined and studied. Estimation of its parameters by moments method, maximum likelihood method and a mixed method are considered. Some examples are given to illustrate the effect on the parameters’ estimates when a non-truncated GPD is used instead of a truncated GPD.

AB - A discrete probability model always gets truncated during the sampling process and the point of truncation depends upon the sample size. Also, the generalized Poisson distribution cannot be used with full justification when the second parameter is negative. To avoid these problems a truncated generalized Poisson distribution is defined and studied. Estimation of its parameters by moments method, maximum likelihood method and a mixed method are considered. Some examples are given to illustrate the effect on the parameters’ estimates when a non-truncated GPD is used instead of a truncated GPD.

KW - Lagrange expansion

KW - Truncated generalized Poisson distribution

KW - estimation

KW - maximum likelihood

KW - ratio of frequencies

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JO - Communications in Statistics - Theory and Methods

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ER -

The Truncated Generalized Poisson Distribution and its Estimation

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Keywords

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