The Harris extended power Lindley distribution: Properties, estimation, and real-world applications

This paper investigates properties of a new parametric distribution generated by the Harris extended family of distributions based on the power Lindley distribution. The probability density function can be decreased, unimodal, and right-skewed shaped. Some various statistical properties are derived including moments, generating function, incomplete moments, moment generating function, lower and upper incomplete moments, and some reliability measures. Estimation of the model parameters by different methods of estimation is discussed. Applications are provided to some real data sets that motivate the flexibility and potentiality of the new model. The performance of the HEPLD is compared with that of thirty competing models such as power Lindley, power length-biased new XLindley, exponentiated power Lindley, transmuted quasi Lindley, power XLindley, exponentiated Weibull Lomax, Weibull Lomax, odd generalized exponential Lomax, alpha power transformed extended power Lindley, exponentiated Lomax, half logistic power Zeghdoud, quasi Lindley, Lindley, power exponentiated Lindley, Zeghdoudi, XLindley, Weibull power Lindley, alpha power transformed Power Lindley, half logistic new-Weibull Pareto, half logistic Weibull, half logistic exponential, half logistic Pareto, power Zeghdoud, exponentiated generalized XLindley, Kumaraswamy Power Lindley, Kumaraswamy Lindley, exponentiated generalized power Lindley, extended Lindley, and Weibull Lindley models.