The EX-Lindley distribution with applications to renewable energy sources data

This study introduces a novel extension of the X-Lindley model, called the EX-Lindley model. The EX-Lindley model is a mixture model that combines the characteristics of the gamma model with the weighted Lindley model. The EX-Lindley model is analyzed to determine various statistical properties, including ordinary moments, inverse moments, moment generating function, incomplete moments, conditional moments, mean deviation, Lorenz, mean residual life, mean inactivity time, order statistics, and extropy. The maximum likelihood method is employed to estimate model parameters using complete data. Moreover, the simulation study is used to compare and evaluate the attributes of the estimations for this generalized model. Finally, two examples of datasets on renewable energy sources are utilized to show the importance of the new model compared to some well-known statistical models.