The Doubly Inflated Poisson and Related Regression Models

<p>Most real life count data consists of some values that are more frequent than allowed by the common parametric families of distributions. For data consisting of only excess zeros, in a seminal paper Lambert (1992) introduced Zero-Inflated Poisson (ZIP) model, which is a mixture model that accounts for the inflated zeros. In this thesis, two Doubly Inflated Poisson (DIP) probability models, DIP (<em>p</em>, λ) and DIP (<em> p</em>1, <em>p</em>2, λ), are discussed for situations where there is another inflated value <em>k</em> > 0 besides the inflated zeros. The distributional properties such as identifiability, moments, and conditional probabilities are also discussed for both probability models. For the data consisting of raw counts as well as grouped frequencies, we have considered parameter estimation using maximum likelihood (ML) and method of moments techniques. Efficiencies show that the ML estimators perform far better than the moment estimators. An application to DIP models is illustrated using data on patients' length of stay in a hospital. Parameter estimation of DIP regression models using maximum likelihood approach is also discussed using data on dental cavities. Finally, we conclude with a brief introduction to two Doubly Inflated Negative Binomial (DINB) distributions and their related regression models.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

2011

Author dc:creator

• Sheth-Chandra, Manasi

Contributors dc:contributor

• N. Rao Chaganty
• Norou Diawara
• Larry Filer
• Dayanand N. Naik

• Doubly inflated Poisson
• Maximum likelihood
• Overdispersion
• Zero-inflated Poisson
• Applied Statistics
• Statistical Models

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Identifier

9781267112590

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1104