Statistical Dependencies Randomized Comparison Of A Number Of Issues

Statistical dependence and stochastic comparison have been provcn to be very useful in applied probability, statistics, reliability, operations research, actuary science, and other fields. This dissertation focus on some preservation properties of location independent risk order and excess wealth order, and some stochastic comparisons of generalized order statistics in the sense of multivariate dispersive order. Regression dependence in latent variable models are also studied.Firstly, we consider the preservation of the location independent risk order under convolution. In the study of increasing risk, location independent risk order can be characterized by comparative statics results, and thc generating process of the order is also given. Based on these results, we establish two sufficient conditions, under which the location independent risk order is preserved under convolution. The excess wealth order is dual to the location independent risk order, so similar results also hold for thc excess wealth order.Secondly, generalized order statistics contain a variety of models of ordered random variables often used in probability and statistics, c.g., ordinary order statistics, record values, k-record values, Pfeifer's record model, progressive type II censored order statistics, order statistics under mulrivariate imperfect repair, and so on. We obtain some stochastic comparisons of generalized order statistics from one sample in terms of Shaked-Shanthikumar multivariate dispersive order, and give some applications of the main results.Finally, to generalize SI, RTI and LTD from bivariate to multivariate case, we introduce three new notions of positive dependence: positive regression dependence (PRD), positive left tail regression dependence (PLTRD), and positive right tail regression dependence (PRTRD). The relationships among the three new notions are studied, as well as the relationships of them to other common used notions of positive dependence. We identify conditions under which the manifest variables T₁,..., T_n possess the new dependence notions for different types of latent variable models. To illustrate the power of our main results, we give some applications in concomitants of order statistics, concomitants of record values, multivariate shock models, and others.