Date of Award

2015

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Avishek Mallick

Second Advisor

Laura Adkins

Third Advisor

Alfred Akinsete

Abstract

A count data that have excess number of zeros, ones, twos or threes are commonplace in experimental studies. But these inflated frequencies at particular counts may lead to over dispersion and thus may cause difficulty in data analysis. So, to get appropriate results from them and to overcome the possible anomalies in parameter estimation, we may need to consider suitable inflated distribution.

In this thesis, we have considered a Swedish fertility dataset with inflated values at some particular counts. Generally, Inflated Poisson or Inflated Negative Binomial distribution are the most common distributions for analyzing such data. Geometric distribution can be thought of as a special case of Negative Binomial distribution. Hence we have used a Geometric distribution inflated at certain counts, which we called Generalized Inflated Geometric distribution to analyze such data. The data set is analyzed, tested and compared using various tests and techniques to ensure the better performance of multi-point inflated Geometric distribution over the standard Geometric distribution.

The various tests and techniques used include comparing the parameters obtained through method of moment estimators and maximum likelihood estimators. The two types of estimators obtained from method of moment estimations and maximum likelihood estimation method, were compared using simulation study, and it is found after the analysis that the maximum likelihood estimators perform better.

Subject(s)

Statistics -- Case studies.

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