Comments on: Progressive censoring methodology: an appraisal

Abstract

Since the mid-90s, when Dr. Balakrishnan together with coauthors Sandhu 1995, 1996; Viveros and Balakrishnan 1994) revisited progressive censoring, a huge number of papers were published dealing with both theoretical and practical aspects. It is one of Dr. Balakrishnan's major scientific merits to reconsider the model of progressive censoring, to see the potential in it, and to advance the methods and properties. His contributions illustrate that progressively Type II censored order statistics are a very useful and powerful model. They lead to a toolbox of properties and statistical procedures, which make the model really applicable. His monograph (Balakrishnan and Aggarwala 2000) on this topic jointly written with R. Aggarwala clearly remains a basic reference work. Now Dr. Balakrishnan provides us with an excellent up-to-date survey on progressive censoring. It impressively illustrates, what has been established in the last decade. We are very pleased to comment on selected topics and to supplement this work, which, of course, can not be exhaustive in some 40 pages. We refer to Dr. Balakrishnan's paper by [B], throughout. Model and distribution theoryThe author points out that progressively Type II censored order statistics are a particular case of generalized order statistics (see Kamps 1995) choosing γ r = k + m − r + m−1 j =r R j , 1 ≤ r ≤ m and k = R m + 1. Hence, the distribution of any choice of progressively Type II censored order statistics can be viewed as a marginal distribution of respective generalized order statistics (see, e.g., (2) in [B]). Thus, the results This comment refers to the invited paper available at: http://dx.