الفهرس 
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Abstract
Arranging a multivariate random sample according to one of its fea- tures results in an ordered model and its concomitants. Motivating by the importance of the concomitants of ordered random variables in applications,we consider, in this thesis, the problem of univariate comparisons of concomitants of generalized order statistics (GOSs) in terms of some partial ordering relations called ”stochastic orders”. Stochastic orders are more informative than comparisons based on single measurements, like means and variances.
Since the concomitants of GOSs can be seen as compound random variables (that is; a mixture of mixed and mixing random variables), we first obtain most of our conclusions in terms of the mixture ran- dom variables, and then the results are translated into the language of concomitants.
This thesis consists of five chapters, organized as follows:
Chapter 1:
In Chapter 1, the basic definitions and theorems used in deriving our main results are mentioned. The literature of stochastic ordering of ordered models and their concomitants is briefly reviewed as well, in Chapter 1.
Chapter 2:
The problem of stochastic comparisons of mixture random variables is discussed in Chapter 2. The assumptions on the ordering of the
mixed and mixing random variables, in the literature are presented. The generated results are used in obtaining comparisons of concomi- tants of GOSs with different parameters, based on the same bivariate distribution. Such problems are called the one-sample comparisons.
Chapter 3:
In Chapter 3, to reflect the dependence between the random variables being compared, we derive stochastic comparison results in terms of the joint stochastic orders. We introduce two new definitions of joint stochastic orders, namely, the joint reversed hazard order and the joint convex order. Moreover, we derive a necessary and sufficient condition for the joint reversed hazard order.Furthermore, the con- comitants of the GOSs are compared in terms of different notions of joint stochastic orders.
Chapter 4:
In Chapter 4, based on the samples that are randomly chosen from two different populations, we derive results that stochastically com- pare the compound random variables. Then, using the obtained re- sults we derive stochastic orderings of the concomitants of GOSs with the same parameters based on two different distributions. Such prob- lems are called the two-sample comparisons.
Chapter 5:
In Chapter 5, the dependence structure of some specific bivariate samples is studied. Precisely, we investigate, for numerous examples of bivariate distributions, the conditions under which we have a posi- tive or/and negative stochastic dependence between the random vari- ables. Additionally, the stochastic comparisons of the concomitants of generalized order statistics, based on these bivariate distribution, are derived, using the results obtained in Chapters 2, 3 and 4.