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 center Xn by subtracting cn and then scale by dn,[6]. This article is focused on finding the norming constants cn and dn for the maxima of the folded normal random variable Xn, where X = |Z|, Z ∼ N(0, 1). We also show that after appropriate normalisation, Xn has a limiting distribution H(x) = exp(− exp(x)), which is the gumbel distribution.