Transmuted Shifted Lindley Distribution: Characterizations, Classical and Bayesian Estimation with Applications

In this article, we propose the quadratic rank transmutation map approach on shifted Lindley distribution to improve the existing distribution further. An additional skewness parameter \(\lambda \) $\lambda$ is incorporated to transmute the distribution. The distribution, hence introduced, is called the Transmuted Shifted Lindley distribution. We provide a comprehensive description of this distribution’s statistical properties and its reliability behavior. The heat maps on the associated parameters are presented. In the estimation section, both maximum likelihood and Bayesian estimation of parameters are discussed. A detailed simulation study is performed. Finally, a real data application illustrates the performance of fitting to the proposed distribution.