Bayesian inference for the log-cosine-power modified Lindley distribution: theory, simulation, and lifetime data application

In this paper, a new three-parameter lifetime distribution is derived from the log-cosinepower-generated family of distributions with the modified Lindley distribution as the baseline. It aims to modify the functionalities of the modified Lindley distribution by using a logarithmic-cosine transformation. Its key mathematical properties are established, and parameter estimation is performed using both maximum likelihood and Bayesian approaches under a variety of loss functions. A simulation study evaluates the performance of the classical and Bayesian estimators using mean squared errors and posterior risks, respectively, supplemented by a diagnostic study with three parallel chains to ensure Markov chain Monte Carlo convergence. In addition, three real data sets are analyzed to demonstrate the flexibility and practical applicability of the new distribution, featuring comprehensive Bayesian inference and prior sensitivity analysis.