A note on estimation of bounds of random variables

Abstract

An estimator and large sample confidence intervals for the upper bound of a random variable are proposed. For the cases considered the estimator is asymptotically considerably more efficient in the sense of smallest mean squared error than the estimators proposed by Robson & Whitlock (1964) and by Cooke (1979). The expected length of the two-sided large sample confidence interval is considerably smaller than the expected length of the corresponding interval proposed by Cooke (1979).