Two new estimators of distribution functions

This paper considers the estimation of a distribution function F_X(x) based on
a random sample X_1, X_2,\ldots , X_n  when the sample is suspected to come from a
close-by distribution F_0(x). Two new estimators, namely F^{PT}_n (x) andF^{S}_n(x) are defined and compared with the ``empirical distribution function'',F_n(x), under local departure; that isF_X(x) = F_0(x) + n^{-1/2}\delta, where\mbox{max}_x |F_X(x) − F_0(x)| \leq n^{-1/2} \delta. In this case, we show thatF^S_n (x)is superior toF^{PT}_n (x)in the neighbourhood ofF_0(x)$.