Asymptotic distributions for weighted power sums of extreme values

Limit laws of weighted power sums of extreme values and Statistical analysis of partition lattices

“…This approach tends to solve Prof. László Zádori's 38-year-old problem on Lattice theory. This dissertation is based on the papers [64], [56], [26] and [63].…”

“…In chapter 3, we pay much attention to the asymptotic normality for the power sums, the consistency, and limit theorems under appropriate assumptions. This chapter is based on a joint paper [64]. Weighted power sums were formulated by considering the necessary and sucient conditions for the existence of normalizing and centering constants.…”

“…The Pickands estimator also can be used to estimate any γ ∈ R, though it suers from high volatility.This chapter is based on a joint paper[64] by the author and L. Viharos. Here we considered proving the asymptotic normality for the weighted power sums over the whole heavy-tail model under some constraints on the weights d i,n .…”