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 $F^{PT}_n (x) and$ F^{S}_n(x) $are defined and compared with the ``empirical distribution function'',$ F_n(x) $, under local departure; that is$ F_X(x) = F_0(x) + n^{-1/2}\delta $, where$ \mbox{max}_x |F_X(x) − F_0(x)| \leq n^{-1/2} \delta $. In this case, we show that$ F^S_n (x) $is superior to$ F^{PT}_n (x) $in the neighbourhood of$ F_0(x)$.

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