Date of Award
8-16-2024
Document Type
Open Access Thesis
Department
Epidemiology and Biostatistics
First Advisor
James Hardin
Abstract
This thesis delves into the double Poisson distribution. Regression based on the double Poisson distribution, as proposed by Efron in 1986, offers an alternative approach that allows for more accurate regression models when dealing with discrete data that exhibit either over- or under-dispersion compared to the Poisson distribution. In this thesis, two methods of calculating the exact double Poisson density are compared: one utilizes the exact probability with the normalizing constant c(mu, theta) by definition or the “finite sum” method, while the other employs an approximation of the normalizing constant c(mu, theta). Furthermore, a simulation was conducted to explore the properties of the double Poisson distribution across various sample sizes and dispersion parameter theta, addressing over-, under-, and equi-dispersed scenarios.
Rights
© 2024, Chao Ma
Recommended Citation
Ma, C.(2024). Simulation Study on Count Data Based on Double Poisson Distribution. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/7740