Generalized logistic model for $r$ largest order statistics, with hydrological application

TL;DR

This paper introduces a new generalized logistic model for the r largest order statistics, improving extreme value analysis by providing a flexible distribution for better quantile estimation in hydrological applications.

Contribution

The paper proposes the rGLO distribution as a novel model for r largest order statistics, extending the rK4D model and enhancing extreme value analysis methods.

Findings

The rGLO model effectively captures extreme value variability.

Simulation studies demonstrate the model's robustness.

Application to streamflow data shows practical utility.

Abstract

The effective use of available information in extreme value analysis is critical because extreme values are scarce. Thus, using the $r$ largest order statistics (rLOS) instead of the block maxima is encouraged. Based on the four-parameter kappa model for the rLOS (rK4D), we introduce a new distribution for the rLOS as a special case of the rK4D. That is the generalized logistic model for rLOS (rGLO). This distribution can be useful when the generalized extreme value model for rLOS is no longer efficient to capture the variability of extreme values. Moreover, the rGLO enriches a pool of candidate distributions to determine the best model to yield accurate and robust quantile estimates. We derive a joint probability density function, the marginal and conditional distribution functions of new model. The maximum likelihood estimation, delta method, profile likelihood, order selection by the entropy difference test, cross-validated likelihood criteria, and model averaging were considered for inferences. The usefulness and practical effectiveness of the rGLO are illustrated by the Monte Carlo simulation and an application to extreme streamflow data in Bevern Stream, UK.