A Mahalanobis Distance‐Based Automatic Threshold Selection Method for Peaks Over Threshold Model

Abstract

AbstractAn unresolved problem in statistical analysis of hydrological extremes (e.g., storms, floods) using POT model is identification of optimal threshold. There are various issues affecting performance of different methods available for threshold selection (TS). To overcome those issues, this study contributes a novel Mahalanobis distance‐based automatic TS method. It involves use of proposed transformation to map Generalized Pareto distributed random variable (depicting peaks over tentative thresholds) from the original space to standard exponential (Exp(1)) distributed random variable in a nondimensional space. Optimal threshold is identified as that which minimizes Mahalanobis distance between L‐moments of the transformed random variable and those of the population (i.e., Exp(1) distribution) in the nondimensional space. Its effectiveness is demonstrated over four existing automatic TS methods through Monte Carlo simulation experiments and case studies over rainfall and streamflow data sets chosen from India, United Kingdom, and Australia. The four methods include three based on goodness of fit (GoF) test statistics (of Anderson‐Darling and two nonparametric tests), and a recent one based on L‐moment ratio diagram whose potential is unexplored in hydrology. This study further provides insight into properties and effectiveness of the four TS methods, which is scanty in literature. Results indicate that there is inconsistency in performance of GoF test‐based methods across data sets exhibiting fat and thin tail behavior, owing to their theoretical assumptions and uncertainty associated with sampling distribution of test statistics. Issues affecting performance of L‐moment ratio diagram‐based TS method are also identified. The proposed method overcomes those issues and appears promising for hydrologic applications.