We establish the equivalence of conditional unbiasedness and Lehmann's risk unbiasedness and a necessary and sufficient condition for the existence of such estimators. This condition brings out transparently the reason for the nonexistence of such estimators in most cases based on single stage...

Let X1,...,Xn be a random sample from an absolutely continuous distribution with non-negative support, and let Y1,...,Yn be mutually independent lifetimes with proportional hazard rates. Let also X(1)...X(n) and Y(1)...Y(n) be their associated order statistics. It is shown that the pair...

Let Rn be the range of a random sample X1,...,Xn of exponential random variables with hazard rate [lambda]. Let Sn be the range of another collection Y1,...,Yn of mutually independent exponential random variables with hazard rates [lambda]1,...,[lambda]n whose average is [lambda]. Finally, let r...