Marshall-Olkin Extended Power Lindley Distribution with Application

Abstract

Lindley distribution was introduced by Lindley (1958) in the context of Bayes inference. 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 Ghitany et al. (2013), called power Lindley distribution. This paper will introduce an extension of the power Lindley distribution using the Marshall-Olkin method, resulting in Marshall-Olkin Extended Power Lindley (MOEPL) distribution. The MOEPL distribution offers a flexibility in representing data with various shapes. This flexibility is due to the addition of a parameter to the power Lindley distribution. Some properties of the MOEPL were explored, such as probability density function (pdf), cumulative distribution function (cdf), hazard rate, survival function, quantiles, and moments. Estimation of the MOEPL parameters was conducted using maximum likelihood method. The proposed distribution was applied to data. The results were given which illustrate the MOEPL distribution and were compared to Lindley, power Lindley, gamma, and Weibull. Model comparison using the log likelihood, AIC, and BIC showed that MOEPL fit the data better than the other distributions.