Author ORCID Identifier
Date Available
5-22-2022
Year of Publication
2020
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Statistics
First Advisor
Dr. Derek Young
Abstract
Statistical intervals (e.g., confidence, prediction, or tolerance) are widely used to quantify uncertainty, but complex settings can create challenges to obtain such intervals that possess the desired properties. My thesis will address diverse data settings and approaches that are shown empirically to have good performance. We first introduce a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals for non-normal distributions. We then turn to zero-inflated data, which are commonly found in, among other areas, pharmaceutical and quality control applications. However, the inference problem often becomes difficult in the presence of excess zeros. When data are semicontinuous, the log-normal and gamma distributions are often considered for modeling the positive part of the model. The problems of constructing a confidence interval for the mean and calculating an upper tolerance limit of a zero-inflated gamma population are considered using generalized fiducial inference. Furthermore, we use generalized fiducial inference on the problem of constructing confidence intervals for the population mean of zero-inflated Poisson distribution. Birnbaum–Saunders distribution is widely used as a failure time distribution in reliability applications to model failure times. Statistical intervals for Birnbaum–Saunders distribution are not well developed. Moreover, we utilize generalized fiducial inference to obtain the upper prediction limit and upper tolerance limit for Birnbaum–Saunders distribution. Simulation studies and real data examples are used to illustrate the effectiveness of the proposed methods.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2020.231
Recommended Citation
Zou, Yixuan, "STATISTICAL INTERVALS FOR VARIOUS DISTRIBUTIONS BASED ON DIFFERENT INFERENCE METHODS" (2020). Theses and Dissertations--Statistics. 47.
https://uknowledge.uky.edu/statistics_etds/47
