Contributions to the theory of stochastic orders

Abstract

This dissertation adds some new results to the theory of stochastic orders. Chapter 1 contains definitions and known results that are related to our study. In Chapter 2, we introduce two new stochastic orders based on ratios of Laplace transforms, and study various properties of the new orders. Among the many properties we discover, the most interesting ones are the relations between the new orders and some existing stochastic orders. In Chapter 3, we obtain various stochastic comparison results of random extrema, that is, the maxima and minima of samples with random sizes. Some results in Chapter 2 find their applications here. In Chapter 4, we study the preservation of various stochastic orders (including the new orders introduced in Chapter 2) under random mapping by point processes. Chapter 5 contains results concerning the preservation of multivariate stochastic orders under shock models. In Chapter 6 we study the preservation of multivariate stochastic orders under random mapping by point processes. Examples and applications of main theorems are presented throughout the dissertation.