Stochastic Comparison Of Second-order Order Statistics Of Dependent Random Variables

Order statistics,as an important concept in statistics,find wide applications in the research of reliability theory,auction theory,and data science.In recent years,significant progress has been made in the study of order statistics for independent random variables.Simultaneously,research on extreme order statistics for dependent random variables has also made noteworthy advancements.The widespread application of second-order statistics has propelled it to the forefront of the reliability statistics domain,capturing extensive attention from the academic community.However,due to the complexity involved in studying second and higher order statistics for dependent random variables,this field of research is still in its nascent stage,leaving several crucial questions unanswered.This thesis focuses on two sets of dependent random variables with a modified proportional hazard rate model.It primarily explores the properties of shochastic orders between second-order statistics of two sets of random variables.The study provides sufficient conditions for the establishment of the usual stochastic order between second-order statistics of dependent heterogeneous random variables.Additionally,it establishes the hazard rate order and the reversed hazard rate order between second-order statistics of two sets of independent heterogeneous random variables.Furthermore,it investigates the hazard rate order and reversed hazard rate order between second-order statistics of random variables with a multivariate outlier model.Finally,the main conclusions of the thesis are illustrated through numerical examples.