Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Rates of convergence for Renyi entropy in extreme value theory

Ali Saeb

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.

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.

Paper Structure

This paper contains 5 sections, 16 theorems, 99 equations.

Table of Contents

  1. Introduction
  2. Rates of convergence for density function
  3. Gumbel domain
  4. Fréchet domain
  5. Rates of convergence for Rényi entropy of max domain of attraction

Key Result

Lemma 2.1

Suppose $F\in\mathcal{D}(\Lambda)$ and (G_h) hold, then

Theorems & Definitions (24)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 3.1
  • proof
  • ...and 14 more