Statistical Analysis of Hourly Solar Radiation in Kumasi –Ghana: Bayesian Approach

Abstract

The solar radiation has been known to have skewed distribution rather than normally distributed irrespective of how large the sample size. The Bayesian statistical analysis of the solar radiation sort to find out from the Bayesian perspective how solar radiation is distributed in Ghana. The paper assumed a beta distribution as the conjugate prior for the solar radiation. The posterior distribution for p where p is the probability of sunshine was determined using the Bernoulli probability distribution. In this paper the random variable X represents the event of having a high or low sunshine base on the threshold of 120kWhm-2 . A randomly selected sample of size of 1500 from each month of the year was used in the analysis. Based on the threshold value the total number of sunshine hours was calculated to help in the computation of posterior beta distribution parameters. The Bayesian analysis from the month of January through December were found to converge both for the prior and posterior mean and variances at a tolerance level of 0.0001 and 0.00001 respectively after twenty iterations. The paper confirms that there are two clusters of which the solar radiation can be placed and that these cluster all converges after twenty iteration. The prior means and posterior mean converges to 0.86000 and .76000 at the tolerance level of 0.0001 respectively while the prior and posterior variances for cluster one and two converged to 6.0E-06 and 4.0E-06 respectively at 0.000001 tolerance level. The papers finally conclude that the clusters have a greater possibility (.86000 and 0.76000) of sunshine. This is also an indication that Kumasi has higher possibility of sunshine.