An Entropy-Based Validation of Threshold Selection Technique for Extreme Value Analysis and Risk Assessment

Extreme value theory is a statistical method for modeling andevaluating risks in peculiar situations that has gainedpopularity in risk management. The main emphasis is on the tailbehavior of the underlying distributions. Threshold selectiontechniques have been extensively used to estimate the extremequantiles or tails of the distribution. An optimal thresholdselection has been an unresolved problem in the peaks overthreshold method of this theory for several decades. Exceedancesabove a certain threshold typically follow the generalized Paretodistribution asymptotically. Our primary goal is to create anefficient threshold selection technique that can be modeled withthe appropriate extreme value distribution to evaluate the sampleof exceedances above an appropriate threshold. In this paper, wepresent a pragmatic automated method for threshold selection basedon the distribution of parameter estimates and evaluationindicator value from entropy-based weighted multiple testingconcepts. A simulation study has been performed to assess itseffectiveness, and the suggested method has been demonstratedthrough the monthly observation of ammonium ion concentration inthe river water dataset.