This paper considers the estimation of a distribution function based on

a random sample when the sample is suspected to come from a

close-by distribution . Two new estimators, namely F^{S}_n(x)F_n(x)F_X(x) = F_0(x) + n^{-1/2}\delta\mbox{max}_x |F_X(x) − F_0(x)| \leq n^{-1/2} \deltaF^S_n (x)F^{PT}_n (x)F_0(x)$.