  Similar to the generalized extreme value (GEV) family, the generalized
extreme value distributions under power normalization are introduced by
Roudsari (1999) and Barakat et al. (2013). In this article, we study the
asymptotic behavior of GEV laws under power normalization and derive
expressions for the kth moments, entropy, ordering in dispersion, rare event
estimation and application of real data set. We also show that, under some
conditions, the Shannon entropy and variance of GEV families are ordered.
