Optimal upper bounds on expected kth record values from IGFR distributions

摘要

The paper concerns the optimal upper bounds on the expectations of the kth record values () centred about the sample mean. We consider the case, when the records are based on the infinite sequence of the independent identically distributed random variables, which distribution function is restricted to the family of distributions with the increasing generalized failure rate (IGFR). Such a class can be defined in terms of the convex orders of some distribution functions. Particularly important examples of IGFR class are the distributions with the increasing density and increasing failure rate. Presented bounds were obtained with use of the projection method, and are expressed in the scale units based on the standard deviation of the underlying distribution function.