Date of Award

2022

Publication Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

Keywords

Discrete data

Supervisor

S.Paul

Supervisor

M.Hlynka

Rights

info:eu-repo/semantics/openAccess

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Discrete data in the form of counts arise in many health science disciplines such as biology and epidemiology. Poisson models are widely used in the regression analysis of count data. The Poisson distribution has a property that the mean and the variance are equal. However in practice many count data sets often display extra-variation or over-dispersion relative to a Poisson model. Thus the Poisson distribution is not an ideal choice for analysing count data in many applications. One very convenient and common model to accommodate this extra dispersion is the two parameter negative binomial distribution. Count data in the form of one-way layout arise in many practical situations. These data often exhibit extra variation that cannot be explained by a simple model, such as the binomial or the Poisson. These data may further be complicated when some of the observations are missing as in the continuous and some other discrete data situations. In this dissertation we study the performance C(α) statistics recommended by Barnwal and Paul (1988) for testing the equality of means of several groups of count data in presence of a common dispersion parameter. We also study the performance of the three C(α) statistics developed by Saha (2008) in terms of level and power. We develop estimation procedures for the parameters involved in the one way layout of count data under different missing data scenarios and study the effect of missingness on the C(α) statistics through simulations.

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