Power Modified Lindley Distribution: Theory and Applications

The power version of the modified Lindley distribution is introduced in this paper, offering a new two-parameter lifetime distribution. As a main interest, it provides a motivated alternative to the Weibull and power Lindley distributions. We discuss its main characteristics and properties, including shapes of the probability density and hazard rate functions, incomplete moments, crude moments, variance, skewness, kurtosis and order statistics. Then, a statistical study of the model is developed. The parameters are estimated by the maximum likelihood method. A simulation study examines the numerical comportment of the bias and mean square error of the maximum likelihood estimates of the parameters. Application of the new model to three data sets is presented, showing that the model has a better fit behavior in comparison to some other well-known lifetime models, including the Weibull and power Lindley models.