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Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs). With the proposed approach, we can systematically derive the joint statistics of any partial sums of ordered statistics, in terms of the moment generating function (MGF) and the probability density function (PDF). Our MGF-based approach applies not only when all the K ordered RVs are involved but also when only the Ks (Ks < K) best RVs are considered. In addition, we present the closed-form expressions for the exponential RV special case. These results apply to the performance analysis of various wireless communication systems over fading channels.

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Many times populations exist which logically must satisfy a stochastic ordering requirement. Nevertheless, estimates of these populations may not bear out this stochastic ordering because of the inherent variability of the observations. This paper will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases (a) one survival being fixed in advance and (b) estimating both survival functions when the data includes censored observations. A numerical example is handled in detail to illustrate the solution to this problem. (Author)

Very often, populations exist that, logically, should satisfy linear stochastic ordering requirements. For example if a mechanical device is improved through N stages, the corresponding survival functions should be linearly stochastically ordered. Nevertheless, estimates may not reflect this stochastic ordering because of the inherent variability of the observations. This document characterizes the maximum likelihood estimates of the survival functions subject to linear stochastic ordering requirements. These estimates may be expressed in terms of the well-known Kaplan-Meier product limit estimates. Also given is an iterative algorithm which must converge to the correct solution that depends only upon solving the pairwise problem. Finally the authors consider an example concerning survival times for people with squamous carcinoma in the oropharynx when classified by degree of lymph node deterioration at time of discovery. (Author)