Available at: https://digitalcommons.calpoly.edu/theses/3008
Date of Award
6-2025
Degree Name
MS in Statistics
Department/Program
Statistics
College
College of Science and Mathematics
Advisor
Bret Holladay
Advisor Department
Statistics
Advisor College
College of Science and Mathematics
Abstract
We study interval estimation for two of the parameters of the negative hypergeometric distribution: (i) the number of successes in a population and (ii) the size of the population. The negative hypergeometric distribution has been relatively overlooked, as the only existing exact procedure that has been applied to it is the analog of the Clopper-Pearson method. To address this gap, we develop several new methods for the negative hypergeometric case, all of which maintain coverage at or above the nominal confidence level. Traditional methods that rely on large sample sizes tend to perform poorly when applied to discrete distributions. In contrast, we construct confidence intervals by reverse-engineering them from an ideal coverage probability function that we establish. We then conduct a comparative analysis of various methods to identify which procedure performs best. Our evaluation criteria include expected and average confidence interval width. We provide a link to a Shiny web app and R package for computing the recommended confidence intervals in practice. Finally, we compare the confidence intervals produced from hypergeometric sampling with those from negative hypergeometric sampling, identifying the scenarios in which each method performs best.