Torres et al. (2026) Influence of Sample Size on the Performance of Methods for Estimating the Parameters of the Gumbel Distribution

Identification

• Journal: Lecture notes in networks and systems
• Year: 2026
• Date: 2026-01-01
• Authors: Mirell G. Piloto Torres, Camila Aldereguía Sánchez, Alberto Gutiérrez de la Rosa, Ingrid Fernández Lorenzo
• DOI: 10.1007/978-3-031-96157-1_9

Research Groups

• Technological University of Havana “Jose A. Echevarría” CUJAE, Marianao, Havana, Cuba
• University of Genoa (DICCA), Genoa, Italy

Short Summary

This study evaluates how sample size influences the performance of five methods (LS, BLUE, MOM, PWM, ML) for estimating the parameters of the Gumbel distribution, commonly used for extreme wind speeds, concluding that sample size is not the sole determinant of method efficacy.

Objective

• To assess how sample size affects the goodness of fit provided by five methods (LS, BLUE, MOM, PWM, and ML) for estimating the parameters of the Gumbel distribution.
• To determine which of these techniques provide superior results for datasets of varying sizes.

Study Configuration

• Spatial Scale: Simulated data; two weather stations in Cuba.
• Temporal Scale: Sample sizes for simulated data range from 10 to 30 data points and 140 to 300 data points. For real data, "past wind speed data collected through instruments" was used, implying a historical observational period.

Methodology and Data

• Models used: Gumbel distribution, Least Squares (LS), Best Linear Unbiased Estimator (BLUE), Method of Moments (MOM), Probability Weighted Moments (PWM), Maximum Likelihood (ML). The Monte Carlo Technique was utilized for data generation and assessment.
• Data sources: Randomly created data (simulated); observational wind speed data collected from two weather stations in Cuba.

Main Results

• The findings indicate that the size of the sample is not the sole factor affecting the performance of the estimation methods on a particular data set.

Contributions

• Provides a comparative assessment of five widely used Gumbel distribution parameter estimation methods (LS, BLUE, MOM, PWM, ML) specifically focusing on the impact of sample size.
• Utilizes a robust evaluation framework based on bias, mean squared error, and joint deficiency criteria.
• Validates the performance of these methods using both extensive Monte Carlo simulations and real-world wind speed data from Cuban weather stations.
• Offers critical insights for practitioners in structural engineering and meteorology regarding the selection of appropriate estimation methods for extreme wind speed analysis, highlighting factors beyond just sample size.

Funding

No explicit funding information was provided in the paper text.

Citation

@article{Torres2026Influence,
  author = {Torres, Mirell G. Piloto and Sánchez, Camila Aldereguía and Rosa, Alberto Gutiérrez de la and Lorenzo, Ingrid Fernández},
  title = {Influence of Sample Size on the Performance of Methods for Estimating the Parameters of the Gumbel Distribution},
  journal = {Lecture notes in networks and systems},
  year = {2026},
  doi = {10.1007/978-3-031-96157-1_9},
  url = {https://doi.org/10.1007/978-3-031-96157-1_9}
}