Date of Award

2016

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Paul, Sudhir

Rights

CC BY-NC-ND 4.0

Abstract

Discrete data in the form of counts arise in many health science disciplines such as biology and epidemiology. The Poisson distribution is the most commonly used distribution for analysing count data. The Poisson distribution has a property that mean and the variance of the distribution are equal to each other. However, in many count data cases this property of the Poisson distribution does not hold as extra dispersion (variation) is observed in the data, and thus Poisson distribution is not an ideal choice for analysing count data in many applications. The presence of extra dispersion in count data is common in many real life situations. To accommodate this extra dispersion situation in count data a well known model is the negative binomial distribution, which is very convenient and common in practice.

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