Journal of Data Science 549-566 , DOI: 10.6339/JDS.201807_16(3).0006 A NEW GENERALIZED TWO PARAMETER LINDLEY DISTRIBUTION * N. Ekhosuehi , + F. Opone and F. Odobaire Department of Mathematics, University of Benin, Benin City, Nigeria. email of authors: *nosakhare.ekhosuehi@uniben.edu; +festus.opone@physci.uniben.edu Abstract:A new generalized two-parameter Lindley distribution which offers more flexibility in modeling lifetime data is proposed and some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, mean residual life function, moment generating function, quantile function, moments, Renyi entropy and stochastic ordering are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimators of the parameters. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit attained by some existing lifetime distributions. Keywords:Lindley Distribution, Hazard rate, Renyi entropy, Moments, Stochastic ordering 1. Introduction Lindley (1958) proposed the Lindley distribution which is a one parameter lifetime distribution in the context of Bayesian statistics, as a counter example of fiducial statistics. A random variable X is said to follow the Lindley distribution with scale parameter θ>0, if the density function is given by (, ) =  2 +1 (1 + ) − ;  > 0,  > 0 (1)