On properties of dependent progressively Type-II censored order statistics

In the context of life-testing, progressive censoring has been studied extensively. But, all the results have been developed under the key assumption that the units under test are independently distributed. In this paper, we consider progressively Type-II censored order statistics (PCOS-II) arising from dependent units that are jointly distributed according to an Archimedean copula. Density and distribution functions of dependent general PCOS-II (GPCOS-II) are derived under this set-up. These results include those in Kamps and Cramer (Statistics 35:269–280, <CitationRef CitationID="CR8">2001</CitationRef>) as special cases. Some bounds for the mean of PCOS-II from dependent data are then established. Finally, through an example, a special case of PCOS-II from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$N$$</EquationSource> </InlineEquation> dependent components is illustrated. Copyright Springer-Verlag Berlin Heidelberg 2013