Ann. Data. Sci. https://doi.org/10.1007/s40745-018-0163-2 Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data Sanku Dey 1 · Indranil Ghosh 2 · Devendra Kumar 3 Received: 10 August 2017 / Revised: 15 March 2018 / Accepted: 28 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract The Lindley distribution has been generalized by many authors in recent years. A new two-parameter distribution with decreasing failure rate is introduced, called Alpha Power Transformed Lindley (APTL, in short, henceforth) distribution that provides better fits than the Lindley distribution and some of its known general- izations. The new model includes the Lindley distribution as a special case. Various properties of the proposed distribution, including explicit expressions for the ordi- nary moments, incomplete and conditional moments, mean residual lifetime, mean deviations, L-moments, moment generating function, cumulant generating function, characteristic function, Bonferroni and Lorenz curves, entropies, stress-strength reli- ability, stochastic ordering, statistics and distribution of sums, differences, ratios and products are derived. The new distribution can have decreasing increasing, and upside- down bathtub failure rates function depending on its parameters. 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 data sets have been analyzed to show how the proposed models work in practice. Keywords Lindley distribution · Moments · Stress-strength reliability · Maximum likelihood estimation B Devendra Kumar devendrastats@gmail.com 1 Department of Statistics, St. Anthony’s College, Shillong, Meghalaya 793001, India 2 Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC, USA 3 Department of Statistics, Central University of Haryana, Mahendragarh, Haryana, India 123