Hybrid Beta-KDE Model for Solar Irradiance Probability Density Estimation

Abstract

This letter proposes a hybrid Beta-kernel density estimation (KDE) model for solar irradiance probability density estimation. The model combines parametric and nonparametric approaches to avoid KDE boundary bias and obtain a more reliable statistical model of solar irradiance. The performance of the hybrid model is assessed via comparisons with the Beta distribution and two KDE models that employ different bandwidth selection methods. The assessment is carried out using the Kolmogorov–Smirnov goodness-of-fit test, and four measures of error: root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and mean bias error (MBE). Results confirm the accuracy of the hybrid model for solar irradiance modeling with percentage improvements over the Beta distribution of up to 13.8% (RMSE), 11.7% (MAE), 19.3% (MAPE), and 72.5% (MBE). The K–S test results show that the proposed Beta-KDE hybrid is the only model for which the null hypothesis is not rejected for any of the eight datasets considered in this study.