Progressively type II censored order statistics, distributions, characterizations and concomitants

In this thesis, distributions, characterizations and concomitants of general models of the ordered random variables such as Progressively Type II censored order statistics are studied. The joint distributions of the nonadjacent Progressively Type II censored order statistics are obtained. A useful identity describing the probability density functions of k nonadjacent Progressively Type II censored order statistics is given. This result is an extension of known results proposed by Balakrishnan, Childs, & Chandrasekar (2002). It is shown that for a particular Progressive Type II censoring scheme with equal withdrawals the joint distributions can be reduced to the distributions of ordinary order statistics. This result allows obtaining characterization theorems for special families of distributions in terms of conditional expected values of Progressively Type II censored order statistics. Characterization theorems for several important classes of distributions are provided in Chapter 4 of this thesis. Also, some goodness-of-fit test procedures based on characterization theorem are described. Keywords: Censoring scheme, Order statistics, Progressively Type II censored order statistics, Goodness-of-fit test, Distribution, Characterization, Concomitant.