New two-parameter XLindley distribution with statistical properties, simulation and applications on lifetime data

Abstract

A novel two-parameter Quasi-XLindley distribution that extends the current XLindley distribution is proposed in this paper. The probability density function of this distribution can be skewed to the left and has symmetric shapes. Mathematical properties of this new distribution are derived including moments and associated shape measures along with reliability properties and actuarial measures. Parameters of this distribution are estimated using different estimation strategies e.g. maximum likelihood, Anderson Darling, maximum product spacing and Cramér-von Mises, Least-squares and weighted Least-squares. A comprehensive simulation study is given to appraise the performance of the suggested estimators. Some real-life data applications of this distribution are also furnished at the end including the data of cancer patients.