FITTING WIND SPEED TO PROBABILITY DISTRIBUTIONS

Abstract

Many researchers have fitted wind speed data to different probability distributions in the world. In Kenya, it is only Weibull distribution with two parameter which have been used to fit the wind speed data. Although, the other distributions like exponential, gamma, normal, log-normal can be the best and more efficient for fitting the wind data and for predicting wind speeds compared to Weibull distribution. Also, Minimum Distance Estimation (MDE) fitting technique is not commonly applied in fitting the two parameters (2-p) and three parameters (3-p) distributions yet it is stated as a better alternative to Maximum Likelihood Estimation (MLE) fitting technique which is considered as the most efficient fitting technique. To achieve this, the study aimed at fitting wind data to a distribution using (MLE) and MDE techniques to help us find the best and efficient probability distribution and most efficient fitting technique. The study used wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The wind speed probability distributions that the data fits best was examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data were fitted to the recommended distributions using MLE and MDE techniques. The best distribution was identified using Akaike's Information Criteria (AIC) and Bayesian Information criteria (BIC). The efficient method or technique and the efficient distribution was investigated using relative efficiency. The results showed that maximum likelihood method is the best and efficient technique for fitting the 2-p distributions and the 3-p distributions. For the comparison of the distributions for the 2-p and 3-p distributions, gamma distribution emerged as the best in all cases under MLE and MDE techniques. Gamma with 3-p distribution gave lower AIC and BIC values hence concluded as the best distribution. The efficiency test showing that gamma distribution with 3-p is more efficient than gamma distribution with 2-p, and also showed that MLE is more efficient than MDE fitting technique. The study concluded that gamma distribution with 3-p is the best and efficient distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 2.071773 and scale parameter of 1.120855.