Power Lindley-G Family of Distributions

In this paper, we introduce a new family of probability distributions generated from a power Lindley random variable called the power Lindley-generated family. The new family extends several classical distributions as well as generalizes the odd Lindley family which is performed by Silva et al. (Austrian J Stat 46:65–87, 2017). Some of the mathematical properties are obtained involving moments, incomplete moments, quantile function and order statistics. New four distributions are provided as special models from the family. The model parameters of the family are estimated by the maximum likelihood technique. An application to real data set and simulation study are provided to demonstrate the flexibility and interest of one special model of the suggested family. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.