Finite Sampling Exponential Bounds

Abstract

This dissertation develops new exponential bounds for the tail of the hypergeometric distribution. It is organized as follows. In Chapter 1, it reviews existing exponential bounds used to control the hypergeometric tail. In Chapter 2, it extends several bounds used to control the binomial tail to the hypergeometric case. In Chapter 3, it describes a basic method to obtain upper bounds for the tail of discrete distributions. In Chapters 3 and 4, it applies this method to the Poisson tail and the hypergeometric tail. In Chapter 5, it proves an improvement to Serfling's inequality in the case of the hypergeometric distribution under constraints on the population proportion and sampling fraction.