Statistical Analysis of Hourly Clearness Index and Diffuse Fraction Data Using Beta Probability Density Functions 

Department of Physics and Technology, Institute of Applied Pedagogy, University of Burundi, Burundi 

Abstract: An analysis of hourly clearness index (k_th) and diffuse fraction (k_dh) data is presented in this paper. Those data have been extracted from a 1-year period records of the hourly global and diffuse solar irradiation on a horizontal surface from a subtropical African station, namely Dakar-Hann (Senegal). The monthly frequency distributions of those data have been firstly constructed and their main characteristics have been derived. Then, the theoretical beta probability functions (β-PDFs) fitting the observed frequency distributions have been implemented. Three complementary statistical tests, i.e., the mean bias error (MBE), the root mean square error (RMSE) and the t-statistics, have been performed to check the effectiveness of the fitting procedure. For any of the twelve monthly sets of k_th and k_dh data, the MBE has been found equal (or close) to zero as expected. The RMSE was much lower than the mean value (of the k_th or k_dh data), and the t-statistics was almost equal to zero or much lower than its critical value (t_c = 3.250). All the obtained β-PDFs are therefore good fits of the corresponding observed monthly frequency distributions of k_th and k_dh data. They should be used consequently as input data in any project of solar energy conversion or storage systems at the considered station. 

Key words: β-PDFs, computation procedure for the basic data, hourly clearness index, hourly diffuse fraction, relative frequency distributions, statistical tests.