A new two-parameter flexible extension of Lindley distribution with variable shapes for hazard rate function

Statistical distributions are important to describe the phenomena in real world. A new two parameter extension of Lindley distribution which called new Lindley (NLi) is intro- duced and studied in details. This model is right skew and left skew in PDF. It isa  unimodal PDF. The hazard rate function of this model is very flexible. Statistically important properties, including the quantile function, asymptotics for the CDF, PDF, and HRF, extreme values, and moments of the new model, are obtained. Parameter estimates process are conducted by the well-known methods of maximum likelihood, weighted least square method Cramér- von Mises method and Anderson Darling method. Tre tables of simulation show that the Anderson Darling method and Cramér von Mises methods are better for estimating the pa- rameters of NLi model. We fit our new model to five real data sets and comapre it with some Lindley extensions and some well-known two-parameter distributions like Gamma, Weibull, Generalized Exponential distribution. The results of tables 12-16 verified that this model is more consistently than other competitive models for real data sets.