Estimating a Distribution Function When New is Better Than Used.
Francisco J. Samaniego, Russell A. Boyles · 1980
The problem we study in this paper is the estimation of the distribution function F under the assumption that F belongs to the class of NBU distributions. Without the NBU restriction, the empirical distribution function F(n) converges to F in several senses and at the best possible rate. However, F(n) need not to be NBU, and, in fact, it is not difficult to show that P(f(n) is NBU) going to 0 when sampling from some NBU distributions (for example, the exponential distribution). Our goal here is to construct a sequence (F(n)) of NBU distributions which achieve the same asymptotic optimality as the sequence (F(n)).