Transcript STATISTICAL TRAINING IN NIGERIA

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INTRODUCTION
The need to use a Poisson-Gamma mixture
distribution arises when the Poisson distribution
exhibits over-dispersion. For the Poisson model,
the mean and the variance are equal.
If the variance of a Poisson model exceeds its
mean, over-dispersion is said to occur. Overdispersion is indicated if Pearson dispersion is
greater than 1 (Hibe, 2007).
The problem with over-dispersion, common to
most Poisson models is that it renders the
parameter estimates biased. Where over-dispersion
is a concern, the alternative models are:
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(i) Quasi-Poisson
(ii) Negative Binomial regression
In this paper, we shall consider only the Negative
Binomial regression as an alternative to the overdispersed Poisson model. In designing an offset
Poisson-Gamma mixture model, it is logical to use
the order listed below:
(i) Poisson distribution
(ii) Gamma distribution
(iii) Poisson-Gamma distribution (Negative Binomial
distribution).
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With profound gratitude, I acknowledge
The Federal University Lafia, Nigeria
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(1)
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(4)
Freund, J. E. (1992). Mathematical Statistics. 5th edition.
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Hilbe, J.M. (2007). Negative Binomial Regression.
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Levin,
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