On the convergence of entropy for K-th extreme

Let recall that the term 'k-th extreme' was introduced in a limiting sense. That is, if $X_{r:n}$ denote the r-th order statistic then for fix k, as $n\to\infty$, $X_{n-k+1:n}$ is called the k-th extremes or k-th largest order statistics. In this paper, we study entropy limit theorems for k-th largest order statistics under linear normalization. We show the necessary and sufficient conditions which convergence entropy of k-th extreme holds.