Recursive Computation and Algorithms

Abstract

In the next two chapters, considerable emphasis will be placed on obtaining moments of progressively Type-II censored order statistics. One reason for this will become clear in Chapters 6 and 10 when the focus is on developing efficient inferential procedures based on progressive Type-II censoring. We have seen in the last chapter that moments of progressively censored order statistics from some distributions can be obtained explicitly. However, very often, it is not possible to obtain explicit expressions for these moments. The idea of obtaining moments of usual order statistics in a recursive manner has been explored for a number of distributions; for example, see Balakrishnan, Malik and Ahmed (1988), and Balakrishnan and Sultan (1998). In this chapter, we establish several recurrence relations satisfied by the single and product moments of progressively Type-II right censored order statistics from the exponential, Pareto and power function distributions as well as their truncated forms. It is important when establishing such recurrence relations that the relations be complete,in the sense that they may be used in a simple recursive manner in order to compute all the single and product moments of all progressively T-II right censored order statistics from the distributions of interest for all sample sizes n and all censoring schemes (R 1,R 2, ⋯, R), m ≤ n. This, in fact, is the case for all the distributions mentioned above.KeywordsOrder StatisticExponential DistributionRecurrence RelationPareto DistributionRecursive AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.