Document Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Program Name/Specialization

Mathematics for Science and Finance

Faculty/School

Faculty of Science

First Advisor

Dr. Zilin Wang

Advisor Role

Supervisor

Second Advisor

Dr. David Soave

Advisor Role

Supervisor

Abstract

This thesis develops likelihood-based methodology for flexible modeling and inference for heterogeneous count data within and adjacent to the Poisson–Tweedie family. A mean–dispersion regression framework is introduced to jointly relate the mean and dispersion to covariates, enabling separation of covariate-driven heterogeneity from distributional parameters. Likelihood inference is implemented using recursive probability mass function evaluation, and performance is assessed through simulation and applications including RNA-sequence counts. The framework is extended to accommodate excess zeros via zero-inflated Poisson–Tweedie models, with full likelihood-based estimation and improved risk estimation illustrated using insurance claim data. Finally, boundary behaviour is investigated through the discrete stable distribution as a limiting case, and nonstandard hypothesis testing is developed using an adjusted likelihood ratio approach supported by simulation and empirical heavy-tailed count analyses.

Convocation Year

2027

Convocation Season

Spring

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