Cubic Rank Transmuted Lindley Distribution with Applications

In this work, we propose a three-parameter generalized Lindley distribution using the cubic rank transmutation map approach by Granzotto et al. (2017). We derive expressions for several mathematical properties including moments and moment generating function, mean deviation, probability weighted moments, quantile function, reliability analysis, and order statistics. We conducted a simulation study to assess the performance of the maximum likelihood estimation procedure for estimating model parameters. The flexibility of the proposed model is illustrated by analyzing two real data sets.