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

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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.

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Code availability

https://github.com/yire-shin/rGLO.git

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Acknowledgements

The authors would like to thank the reviewers and the Associate Editor for their valuable comments and constructive suggestions.

Funding

This research was supported by Basic Science Research Program (No.RS-2023-00248434, 2020R1I1A3069260) and BK21 FOUR (No. 5120200913674) through the National Research Foundation of Korea funded by the Ministry of Education.

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  1. Department of Mathematics and Statistics, Chonnam National University, Gwangju, 61186, Korea

    Yire Shin & Jeong-Soo Park

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  1. Yire Shin
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Correspondence to Jeong-Soo Park.

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Shin, Y., Park, JS. Generalized logistic model for r largest order statistics, with hydrological application. Stoch Environ Res Risk Assess 38, 1567–1581 (2024). https://doi.org/10.1007/s00477-023-02642-7

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