Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution
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 perfo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/14/2295 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839615654700777472 |
|---|---|
| author | Autcha Araveeporn |
| author_facet | Autcha Araveeporn |
| author_sort | Autcha Araveeporn |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-af5b4e034b444fc38bbe9c4f99ae6cc8 |
| institution | Matheson Library |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-af5b4e034b444fc38bbe9c4f99ae6cc82025-07-25T13:29:05ZengMDPI AGMathematics2227-73902025-07-011314229510.3390/math13142295Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value DistributionAutcha Araveeporn0Department of Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandThis 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.https://www.mdpi.com/2227-7390/13/14/2295generalized extreme valuemaximum likelihood estimationprobability-weighted momentstwo-stage order statistics |
| spellingShingle | Autcha Araveeporn Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution Mathematics generalized extreme value maximum likelihood estimation probability-weighted moments two-stage order statistics |
| title | Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution |
| title_full | Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution |
| title_fullStr | Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution |
| title_full_unstemmed | Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution |
| title_short | Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution |
| title_sort | improved probability weighted moments and two stage order statistics methods of generalized extreme value distribution |
| topic | generalized extreme value maximum likelihood estimation probability-weighted moments two-stage order statistics |
| url | https://www.mdpi.com/2227-7390/13/14/2295 |
| work_keys_str_mv | AT autchaaraveeporn improvedprobabilityweightedmomentsandtwostageorderstatisticsmethodsofgeneralizedextremevaluedistribution |