Estimates Based on Sequential Order Statistics with the Two-Parameter Pareto Distribution

This paper deals with the concept of sequential order statistics (SOS) for modeling the sequential r-out-of-n: F systems under a conditional proportional hazard rates drawn from a two-parameter Pareto distribution. Maximum likelihood estimates of parameters of interest are investigated based on multiple SOSs. Proposing various priors for the parameters of the assumed model, the Bayes estimates of the parameters of interest are derived and admissibility of obtained estimators is investigated. Due to the lack of explicit expressions for some of the obtained Bayes estimates, Lindley's approximations are derived. To assess the performance of the obtained estimators, we conducted extensive simulation studies.