A new generalization of Lindley distribution for modeling of wind speed data

Abstract

The most suitable source of energy for human use is wind energy, which is competitive and supports the energy demand of a large population. In this study, we introduced a new probability distribution for the analysis of wind speed data. The newly developed distribution is known as “New Alpha power transformed power Lindley”. Some mathematical properties of the proposed distribution were derived including reliability function, failure rate, moments and associated measures, quantile function. The model parameters were estimated using the maximum likelihood approach. The performance of the estimation method was assessed via a simulation study. The wind speed datasets were analyzed using new distribution and compare its modeling performance with eleven renowned generalizations of Lindley distributions (Lindley, power Lindley, Marshall–Olkin Lindley, exponentiated Lindley, Pseudo Lindley, Quasi Lindley, Gamma Lindley, generalized inverse Lindley, extended Lindley, exponentiated power Lindley, extended inverse Lindley and extended power Lindley). To good fitting probability distribution function, log-likelihood, root mean square error, coefficient of determination, Akaike Information Criteria for each distribution have been calculated. Additionally, estimated density and cdf curves were fitted over the observed wind speed dataset. Findings showed that the proposed distribution provides the best fitting according to model selection criteria. On the other hand, exponentiated power Lindley and extended power Lindley distribution are the next best distributions for modeling wind speed data for selected stations. Overall, outcomes show the practicality, accuracy, and adequacy of the newly proposed distribution depicting wind energy data.