On the Approximation of a Distribution Function by an Empiric Distribution

Abstract

Let $x_1, \cdots, x_n$ be independent chance variables with the common distribution function $F(x)$ and the empiric distribution function $F^\ast(x)$. Let $a_n$ be the value of $a$ which minimizes (1) below. In this paper the asymptotic distribution of $\sqrt{n} a_n$ is obtained, subject to certain restrictions on $F(x)$.