INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res., 22, 833 — 842 (1998) APPLICATION OF PROBABILITY MODELS TO MALAYSIAN SUNSHINE DATA M. YUSOF SULAIMAN*, W. M. HLAING OO, MAHDI ABD. WAHAB AND AZMI ZAKARIA Physics Department, Faculty of Science and Environmental Studies, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia SUMMARY A 10-year Malaysian sunshine data of four stations were fitted to three models, namely the Bendt, Hollands and Huget and Saunier models. Distribution parameters of the models were determined from the values of the observed mean of the sunshine data. The Kolmogorov—Smirnov test was applied to determine the goodness of fit. It was found that the Saunier model was suitable for the Petaling Jaya and Subang stations while the Hollands and Huget model well suited the Bayan Lepas and Kota Bharu stations. The Bendt model did not give a good fit for all stations. It was also found that for the months that have the same observed mean but different observed standard deviations the distribution models were able to fit well only if the estimated standard deviations were close in value to the observed standard deviations.  1998 John Wiley & Sons, Ltd. KEY WORDS sunshine duration; clearness index; probability density function; cumulative distribution function 1. INTRODUCTION In predicting a long-term average energy delivery of solar collectors, information on the fraction of the total available solar irradiation exceeding a certain threshold, incident upon a collector aperture for a specified period of time must be made available. In the past, many models to calculate this quantity referred to as utilizability (Hottel and Whidler, 1955; Klein, 1978; Collares-Pereira and Rabl, 1979a, b; Gordon and Zarmi, 1983a, b), relied on the frequency distribution of irradiation or some irradiation-related parameters. As early as 1960, Liu and Jordan (1960) had analysed sets of hourly and daily solar irradiation data taken at a fixed location and for a fixed month of the year. Their generalized cumulative distribution functions (CDF), F (K  , K M  ) of the clearness index K  corresponding to a monthly average K M  were observed to be independent of location and month. Since then, their functions were widely used by researchers all over the world. In another approach, using arguments of statistical mechanics, Bendt et al. (1981) derived the generalized distribution functions, which agreed well with experimental data for 90 stations in the contiguous United States with approximately 20 years of observation. Their probability density function (PDF) took the following form: P (K  , K M  )"C exp(K  ) (1) where C is a normalization constant and the parameter  depends on K  . On closer examination, equation (1) does not seem to describe a realistic distribution since the probability of observing the maximum value of the clearness index, K  is always a maximum. To overcome this problem, Hollands and Huget (1983) * Correspondence to: Dr. M. Y. Sulaiman, Physics Department, Faculty of Science and Environmental Studies, Universiti Putra Malaysia, 43400 UPM, Serdang Selangor, Malaysia. Email: myusof@fsas.upm.edu.my CCC 0363—907X/98/090833 — 10$17.50 Received 7 October 1997  1998 John Wiley & Sons, Ltd. Accepted 22 December 1997