The Properties And Application Of Some Stochastic Orderings

Stochastic orderings are important decision-making tools in the fields of statistics,risk management and information science,which characterizes the quantitative comparison be-tween random variables in a certain mathematical sense.By studying the stochastic ordering,we can get a better understanding of people's preferences,so as to analyze and guide people's decision-making better.In real life,due to the complexity of the data,the skew normal distribution is more flexible than the normal distribution in the fitting of real data,and more comprehensive and accurate information can be obtained.Therefore,in recent years,the skew normal distri-bution has been widely used,whose stochastic orderings are of great research value.This paper mainly uses some kinds of stochastic orderings to discuss the stochastic comparison of random variables subject to the skew normal distribution and obtains the necessary and sufficient conditions for the relationship between various stochastic orderings of skew normal distribution and its distribution parameters.The first chapter introduces the research background and current situation of this paper.Then,the second chapter mainly introduces the definition,the nature and the relationship of several kinds of stochastic orderings,such as stochastic dominance,convex order,stop-loss order and so on,and briefly introduces their mathematical meanings.In the third chapter,we introduce the knowledge of skew normal distribution.In the fourth chapter,we prove the necessary and sufficient conditions for several kinds of stochastic orderings of one-dimensional skew normal distributions,and later generalize an identity for multivariate normal distribu-tions found by Miiller[12]to multivariate skew normal distributions,and use this identity to discuss these stochastic orderings of multivariate skew normal distributions,which is the main results of this paper.Finally,some issues that deserve further study are presented in the fifth chapter.