Marshall-Olkin extended inverse power Lindley distribution with applications

The Lindley distribution was introduced by Lindley in the context of Bayes inference.1 Its density function is obtained by mixing the exponential distribution, with scale parameter β, and the gamma distribution, with shape parameter 2 and scale parameter β. Recently, a new generalization of the Lindley distribution was proposed by Barco et al., called the inverse power Lindley distribution. 2 This paper will introduce an extension of the inverse power Lindley distribution using the Marshall-Olkin method, resulting in the Marshall-Olkin Extended Inverse Power Lindley (MOEIPL) distribution. The MOEIPL distribution offers a flexibility in representing data with various shapes. This flexibility is due to the addition of a tilt parameter to the inverse power Lindley distribution. Some properties of the MOEIPL are explored, such as its probability density function, cumulative distribution function, hazard rate, survival function, and quantiles. Estimation of the MOEIPL parameters was conducted using maximum likelihood method. The proposed distribution was applied to model the wind speed in Demak, Indonesia. The results illustrate the MOEIPL distribution and arre compared to Lindley, power Lindley, inverse Lindley, inverse power Lindley, gamma, and Weibull. Model comparison using the AIC shows that MOEIPL fits the data better than the other distributions.