Kotz Distribution Of Some Sequence Relationship And Its Related Inequalities,

Kotz type distribution is an important kind of elliptically symmetric distributions. It was first introcuced by Kotz, S. in 1975. As a generalization of multinormal distribution, Kotz type distributon constructs many models to which the usual normality assumption is not applicable. In addition, Kotz type distribution also has an extensive application in the fields such as economic mathematics, repeated measurement, and so on.Stochastic order is a hot research topic in the field of probability which mainly compares the expectations of two random vectors about some function groups. Therefore, it plays an important role in both theoretical and applied fields.The main achievement of this dissertation is to have obtained a series of sufficiency and/or necessity conditions of stochastic orders about Kotz type distribution. This dissertation also extends the correlation inequalities of multinormal distribution to that of Kotz type distribution.The introduction first has a literature review of Kotz type distribution. Then it discusses the significance of the research of stochastic orders, and the research development of the correlation inequalities of multinormal distribution.The second chapter based on introducing the parameter A and lining each of the parameters, gives an important identity for Kotz type distribution, which becomes the basis of the research of stochastic orders for Kotz type distribution.The third chapter first gives the definition of some important stochastic orders, and then gives the sufficiency and/or necessary conditions of corresponding stochastic orders according to the identity given in chapter two.The fourth chapter deals with the Peak order of Kotz type distribution. We can not obtain the conclusion using Anderson Theory directly because the unimodal condition could not be satisfied if the parameter k doesn't equal one. However, with the identity given in chapter two, we can give the sufficiency and necessity condition of Peak order for uni-dimensional Kotz type distribution even k 1.In the last chapter, the author verifies the log-concave property of Kotz type distribution and uses it to obtain the correlation inequalities of Kotz type distribution.