#### Date of Award

Summer 2014

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics and Statistics

#### Program/Concentration

Computational and Applied Mathematics

#### Committee Director

N. Rao Chaganty

#### Committee Member

Norou Diawara

#### Committee Member

Michael Doviak

#### Committee Member

Miguel Padilla

#### Abstract

Count data are common in observational scientific investigations, and in many instances, such as twin or crossover studies, the data consists of dependent bivariate counts. An appropriate model for such data is the bivariate Poisson distribution given in Kocherlakota and Kocherlakota (2001). However, in situations where inflated count of (0, 0) occur, Lee et al. (2009) proposed the zero-inflated bivariate Poisson distribution which accounts for the inflated count. In this research, we introduce and study a bivariate distribution that accounts for an inflated count of the (*k*, *k*) cell for some *k*>0, in addition to the inflated count for the (0, 0) cell. This bivariate doubly inflated Poisson distribution (BDIP) is a parametric model determined by four parameters (*p*, λ 1, λ2, λ3). In this dissertation, we will first discuss the distributional properties such as identifiability, moments and conditional distributions and stochastic representation of the BDIP model. Next, we will discuss parameter estimation by the method of moments and maximum likelihood methods and a comparison of the methods via asymptotic relative efficiency calculations. We also discuss the BDIP regression model that incorporates covariates into the BDIP model. We illustrate applicability of the BDIP regression model to analyze a subset of the Australian health survey data. Finally we conclude with an introduction to BDIP2 distribution, defined by the parameters (*p*1, *p* 2, λ1, λ2, λ3), and corresponding regression models.

#### DOI

10.25777/pj3y-3255

#### ISBN

9781321316551

#### Recommended Citation

Sengupta, Pooja.
"Bivariate Doubly Inflated Poisson and Related Regression Models"
(2014). Doctor of Philosophy (PhD), dissertation, Mathematics and Statistics, Old Dominion University, DOI: 10.25777/pj3y-3255

https://digitalcommons.odu.edu/mathstat_etds/59