Rates of convergence for Renyi entropy in extreme value theory

Abstract

Max stable laws are limit laws of linearly normalized partial maxima of independent identically distributed random variables. Saeb (2014) proves that the Renyi entropy of order b (b > 1) of linear normalized maximum of iid random variables with continuous differentiable density is convergent to the Renyi entropy of order b of the max stable laws. In this paper, we study the rate of convergence result for Renyi entropy for linearly normalized partial maxima.