ON HOW TO FIND THE NORMING CONSTANTS FOR THE MAXIMA OF A FOLDED NORMALLY DISTRIBUTED VARIABLE

Abstract

A general procedure when one is looking for a limiting distribution of Xn =
max(X1; : : : ;Xn) is to first centerXn by subtracting cn and then scale by dn (Mood et al.,
1974). This article is focused on finding the norming constants cn and dn for the maxima of
the folded normal random variable Xn, where X = jZj; Z N(0; 1). We also show that
after appropriate normalisation, Xn has a limiting distribution H(x) = exp(