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Thesis
Reparameterization of the Poisson Distribution and Applications
University of West Florida Libraries
Master of Science (MS), University of West Florida
2024
Abstract
This thesis studied the reparameterized distribution derived from the Poisson distribution, aimed at addressing limitations in traditional count data modeling techniques. The reparameter- ized distribution is characterized by a novel probability mass function (pmf) and cumulative dis- tribution function (cdf). We thoroughly explore the statistical properties of this new distribution, including its moments, moment generating functions, skewness, kurtosis, Re ́nyi entropy, hazard rate function, and additional properties.Six parameter estimation techniques are investigated: uniformly minimum variance unbi- ased estimator (UMVUE), maximum likelihood estimation (MLE), method of moments (MOM), Bayesian Estimation (BE), least squares (LS), and weighted least squares (WLS). These methods are evaluated using Monte Carlo simulations to ensure their robustness and accuracy.
The practical applicability of the reparameterized distribution is demonstrated through its ap- plication to three urban bike datasets: the New York City East River Bicycle Crossings dataset, the Montreal Bike Lanes dataset, and the bike sharing dataset. A generalized linear model based on the reparameterized distribution is constructed, and its performance is compared with stan- dard Poisson and negative binomial regression models. Various evaluation metrics are employed, with cross-validation used to further assess predictive performance. Results indicate that the new generalized linear model performs favorably compared to Poisson and negative binomial regres- sion models in fitting count data. The reparameterized distribution presents a viable alternative to traditional models, offering particular advantages in specific contexts of count data analysis.
Details
- Title
- Reparameterization of the Poisson Distribution and Applications
- Resource Type
- Thesis
- Contributors
- Subhash Bagui (Committee Chair)Jia Liu (Committee Member)Shusen Pu (Committee Member)
- Publisher
- University of West Florida Libraries
- Format
- pdf
- Number of pages
- 60
- Copyright
- © 2024 Mingfang Huang
- Identifiers
- 99380569797106600
- Academic Unit
- Mathematics and Statistics
- Language
- English
- Awarding Institution
- University of West Florida; Master of Science (MS)
- Theses and Dissertations
- Master of Science (MS), University of West Florida