A three-parameter Lindley distribution, which includes some two-parameter Lindley distributions introduced by Shanker and Mishra (2013 a, 2013 b), Shanker et al (2013), Shanker and Amanuel (2013), two-parameter gamma distribution, and one parameter exponential and Lindley distributions as special cases, has been proposed for modeling lifetime data. Its statistical properties including its shape, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic ordering, mean deviations, order statistics, Renyi entropy measure, Bonferroni and Lorenz curves, stress-strength reliability have been discussed. For estimating its parameters, maximum likelihood estimation has been discussed. Finally, a numerical example has been presented to test the goodness of fit of the proposed distribution and the fit has been compared with the three-parameter generalized Lindley distribution.
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