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Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution

Author

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  • Autcha Araveeporn

    (Department of Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

Abstract

This study evaluates six parameter estimation methods for the generalized extreme value (GEV) distribution: maximum likelihood estimation (MLE), two probability-weighted moments (PWM-UE and PWM-PP), and three robust two-stage order statistics estimators (TSOS-ME, TSOS-LMS, and TSOS-LTS). Their performance was assessed using simulation experiments under varying tail behaviors, represented by three types of GEV distributions: Weibull (short-tailed), Gumbel (light-tailed), and Fréchet (heavy-tailed) distributions, based on the mean squared error (MSE) and mean absolute percentage error (MAPE). The results showed that TSOS-LTS consistently achieved the lowest MSE and MAPE, indicating high robustness and forecasting accuracy, particularly for short-tailed distributions. Notably, PWM-PP performed well for the light-tailed distribution, providing accurate and efficient estimates in this specific setting. For heavy-tailed distributions, TSOS-LTS exhibited superior estimation accuracy, while PWM-PP showed a better predictive performance in terms of MAPE. The methods were further applied to real-world monthly maximum PM2.5 data from three air quality stations in Bangkok. TSOS-LTS again demonstrated superior performance, especially at Thon Buri station. This research highlights the importance of tailoring estimation techniques to the distribution’s tail behavior and supports the use of robust approaches for modeling environmental extremes.

Suggested Citation

  • Autcha Araveeporn, 2025. "Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution," Mathematics, MDPI, vol. 13(14), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2295-:d:1703845
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    References listed on IDEAS

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    1. Bashir Ahmed Albashir Abdulali & Mohd Aftar Abu Bakar & Kamarulzaman Ibrahim & Noratiqah Mohd Ariff & Alessandro De Gregorio, 2022. "Extreme Value Distributions: An Overview of Estimation and Simulation," Journal of Probability and Statistics, Hindawi, vol. 2022, pages 1-17, October.
    2. Bali, Turan G., 2003. "The generalized extreme value distribution," Economics Letters, Elsevier, vol. 79(3), pages 423-427, June.
    3. Frederico Caeiro & Ayana Mateus, 2023. "A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    4. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    5. Amal Helu, 2022. "The principle of maximum entropy and the probability-weighted moments for estimating the parameters of the Kumaraswamy distribution," PLOS ONE, Public Library of Science, vol. 17(5), pages 1-21, May.
    6. Candia, Claudio & Herrera, Rodrigo, 2024. "An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile," Journal of Empirical Finance, Elsevier, vol. 77(C).
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