Abstract
In this paper, we present a new weighted Poisson distribution for modeling underdispersed count data. Weighted Poisson distribution occurs naturally in contexts where the probability that a particular observation of Poisson variable enters the sample gets multiplied by some non-negative weight function. Suppose a realization y of Y a Poisson random variable enters the investigator’s record with probability proportional to w(y): Clearly, the recorded y is not an observation on Y, but on the random variable Yw, which is said to be the weighted version of Y. This distribution a two-parameter is from the exponential family, it includes and generalizes the Poisson distribution by weighting. It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000). We present some moment properties and we estimate its parameters. One classical example is considered to compare the fits of this new distribution with the extended Poisson distribution.
Highlights
The Poisson distribution is considered the standard distribution for the analysis of count data
It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000)
We can quote the negative binomial distribution, used since Greenwood and Yule in 1920, the weighted Poisson distribution proposed by Castillo and PerezCasany in 1998, the generalization of the Poisson distribution proposed by Consul in 1989, etc
Summary
The Poisson distribution is considered the standard distribution for the analysis of count data. Data from Kendall in 1961 follow several distributions underdispersed in particular the extended Poisson distribution proposed by Dimitrov and Kolev in 2000. The main goal of this paper is to propose another underdispersed distribution that better describes Kendall’s data and to compare it with the extended Poisson distribution.
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