Predictions of Order and Record Statistics

Abstract

In this chapter we evaluate expected increments of future order and record statistics in the i.i.d. samples under conditions that some previous values are known. These are important for predicting prospective failures in reliability systems and shock models on the grounds of former data. The results are based on representations of conditional expectations of order statistics and records in terms of unconditional expectations of other ones presented in Section 2.2, and evaluations of the latter derived in Sections 4.1, 4.2, 6.2, and 6.3.