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

Autcha Araveeporn ()
Additional contact information
Autcha Araveeporn: Department of Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Mathematics, 2025, vol. 13, issue 14, 1-20

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.

Keywords: generalized extreme value; maximum likelihood estimation; probability-weighted moments; two-stage order statistics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/14/2295/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/14/2295/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:14:p:2295-:d:1703845

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().