Determination of Probability Distribution Function for Modelling Global Solar Radiation: Case Study of Ibadan, Nigeria

In this paper, the most probable probability distribution for modelling the global solar radiation of Ibadan is determined. The data used for the analysis consists of daily average global solar radiation collected from International Institute of Tropical Agriculture (IITA) located in Ibadan. The data span over the periods of nine years (2000-2008). Various distribution functions are tested and most suitable one is determined using four different goodness of fit test. The parameters of the best fitted distribution are calculated and the variations in the characteristic of the global solar radiation are clearly shown. Some of the key results show that logistic distribution present the best probability distribution for modelling global solar radiation of Ibadan with Root Mean Square Error (RMSE) of 0.399 MJ/m^2/day, Mean Absolute Error (MAE) of 0.214 MJ/m^2/day, Mean Absolute Percentage Error (MAPE) of 3.26% and coefficient of determination (R^2) of 0.989. The location and the scale parameter for the distribution varies over a wide range from season to season and year to year: The location parameter varies from 8.25 MJ/m^2/day in August 2001 to 18.58 MJ/m^2/day in March 2001 and the scale parameter ranges from 0.61 in February 2003 to 4.19 in July 2007. The month of August present the lowest mean global solar radiation in most of the years. This paper is useful as first-hand information in the prediction of future global solar irradiation for Ibadan having known the past behavior and for fixing the missing data.