Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference

The Lindley distribution has been generalized by many authors in recent years. A new two-parameter distribution is introduced, called Alpha Power Transformed Lindley (aP T L) distribution that provides better fit than the Lindley distribution and some of the well known distributions. The new model includes the Lindley distribution as a special case. Several properties of the proposed distribution, including explicit expressions for the ordi- nary moments, incomplete and conditional moments, mean residual lifetime, mean devia- tions, L-moments, moment generating function, cumulant generating function, characteris- tic function, Bonferroni and Lorenz curves, entropies, stress-strength reliability, stochastic ordering, statistics and distribution of sums, differences, ratios and products are derived. The new distribution can have decreasing and increasing failure rates function depending on its parameters. The estimates of the model parameters are obtained by the method of maximum likelihood estimation. Also, we obtain the confidence intervals of the model parameters. A simulation study is carried out to examine the bias and mean squared error of the maximum likelihood estimators of the parameters. Finally, two earthquakes data sets have been analyzed to show how the proposed models work in practice