  Max stable laws are limit laws of linearly normalized partial maxima of
indepen- dent, identically distributed (iid) random variables (rvs). These are
analogous to stable laws which are limit laws of normalized partial sums of iid
rvs. In this paper, we study entropy limit theorems for distribution functions
in the max domain of attraction of max stable laws under linear normalization.
More specifically, we study the problem of convergence of the Shannon entropy
of linearly normalized partial maxima of iid rvs to the corresponding limit
entropy when the linearly normalized partial maxima converges to some
nondegenerate rv. We are able to show that the Shannon entropy not only
converges but, in fact, increases to the limit entropy in some cases. We
discuss several examples. We also study analogous results for the k-th upper
extremes.
