On how to find the norming constants for the maxima of a folded normally distributed variable

A general procedure when one is looking for a limiting distribution of $X_n = max(X_1,\ldots, X_n)$ is to first center $X_n$ by subtracting $c_n$ and then scale by $d_n$ (Mood et al.,1974). This article is focused on finding the norming constants $c_n$ and $d_n$ for the maxima of
the folded normal random variable $X_n$ , where $X = |Z|$ , $Z\sim N(0, 1)$ . We also show that
after appropriate normalisation, $X_n$ has a limiting distribution $H(x) =\ exp(\exp(x))$ ,
which is the Gumbel distribution.

46n1_3

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