Optimal Bandwidth Selection Methods with Application to Wind Speed Distribution

Gündüz N., Karakoç Ş.

MATHEMATICS, vol.11, no.21, pp.1-21, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 21
  • Publication Date: 2023
  • Doi Number: 10.3390/math11214478
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1-21
  • Gazi University Affiliated: Yes


Accurate estimation of the unknown probability density functions of critical variables, such as wind speed-which plays a pivotal role in harnessing clean energy-is essential for various scientific and practical applications. This research conducts a comprehensive comparative analysis of seven distinct bandwidth calculation techniques across various normal distributions, using simulation as the evaluation method in the context of Kernel Density Estimation (KDE). This analysis includes the calculation of the optimal bandwidth and assessment of the performance of these methods with respect to Mean Squared Error (MSE), bias, and the optimal bandwidth value. The findings reveal that among the various bandwidth methods evaluated, the Bandwidth bandwidth-based Cross-Validation (BCV), especially for small sample sizes, consistently provides the closest result to the optimal bandwidth across most of the applied normal distributions. These results provide valuable insights into the selection of optimal bandwidths for accurate and reliable density estimation in the context of normal distributions. Another key aspect of this work is the extension of these methods to wind speed data in a specific region. Monthly wind speed kernel density estimates obtained using all seven bandwidth selection techniques show that Smoothed Cross-Validation (SCV) is suited for this type of real-world data.