The odd Weibull Lindley distribution for modeling wind energy data

In this paper, a novel distribution termed the odd Weibull Lindley distribution is formed by combining the Lindley distribution with the odd Weibull family. Its probability density function and cumulative distribution function are obtained. The mixture representation of this novel distribution is obtained to calculate the properties easily. The reliability measures and statistical properties like moments, median, and mode are derived. Moment-generating function, inverted moments, incomplete moments, probability-weighted moments, stochastic ordering, and order statistics are studied. The quantile function of the proposed distribution is also studied to generate random variables. The parameter values of the distribution are obtained using the MLE method, which is inferred by the Monte Carlo simulation study on the proposed distribution. The adequacy of the proposed distribution is studied by utilizing the wind energy data generated by four major companies in Germany. The measures such as p value, AIC, BIC, and HQIC are obtained to check the fitness of the proposed distribution compared to other baseline distributions such as odd Weibull inverse Topp-Leone distribution, power exponentiated Lindley distribution, Weibull distribution, Lindley distribution, and exponential distribution.