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
Summary
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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