Optimal evaluations for the bias of trimmed means of $$k$$ k th record values

Abstract

We provide sharp upper and lower mean-variance bounds on the expectations of trimmed means of kth record values from general family of distributions. Also we improve these bounds in the case of non-trimmed means for parent distributions with decreasing density or decreasing failure rate. They can be viewed as bounds on the bias of approximation of expectation of the parent population by mean or trimmed mean of record values. The results are illustrated with numerical examples.