Abstract

A New Methodology for the Block Maxima Approach in Selecting the Optimal Block Size

Highlights

  • Predicting the probability of extreme and rare events is important for making future inferences

  • Many researchers have designed methodologies related to the block size dilemma in relation to the Block Maxima (BM) method

  • In most of the studies related to this topic, we could not reach any reasons or assumptions that explain why they chose the block size they used in their studies

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Summary

Introduction

Predicting the probability of extreme and rare events is important for making future inferences. The extreme value theory (EVT) is a robust technique used to analyse the tail behaviour of distributions. Fisher and Tippett developed EVT [1]. It was later formalized by Gnedenko [2]. After the theoretical developments between 1930s and 1940s, lots of papers related to the applications of EVT have been used with different scientific fields (e.g., engineering, finance (McNeil, 1999) [3], environment (Smith, 1989; Stephenson et al, 2005) [4], [5]). With EVT, let X1, X2, X3,..., Xn be identically and independently distributed random variables. The main theory of the extreme data is about the limit behaviour of the max{X1, X2, X3,..., Xn} or min {X1, X2, X3,..., Xn} as nn → ∞ [6]

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