Comparison of Weibull Distribution and Exponentiated Weibull Distribution Based Estimation of Mean and Variance of Wind Data

Wind speed is the most important parameter in the design and study of the environmental impact assessment. The wind speed determines the concentration of any toxic pollutant released from any chemical industry. As the wind speed increases the concentration of the toxic pollutant at any location in the environment at any instant of time decreases. It is also known that as the wind speed increases the cost of the wind energy is reduced. Literature study reveals that the probability distribution of wind speed can be presented by Weibull distribution and it has been accepted so without any statistical investigations. In this study, it is being proposed that similar to Weibull distribution, a better fitting of wind speed data is possible by Exponentiated Weibull distribution. Statistical investigations as an evidence of this proposition via estimation of mean and variance of wind speed data by fitting through both Weibull and Exponentiated Weibull distributions are presented in this paper. A comparison of the representative estimates through respective probability distributions is also presented in this study. Estimation of parameters (shape and scale) of both the distributions is presented by using maximum likelihood algorithm.