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.

The coefficient of variation (CV) is a frequently used standardized measure of variability that allows meaningful comparison among datasets measured using different scales or units. Although widely applied in practice, formal statistical inference for the CV under non-normal distributions has received limited attention. This study focuses on estimating the CV for the weighted exponential distribution under an adaptive Type-II hybrid progressive censoring scheme, which enhances the efficiency of life-testing experiments by balancing test duration and the number of observed failures. Both Bayesian and non-Bayesian frameworks are considered. Point estimation in the non-Bayesian framework is carried out using the maximum likelihood method, whereas interval estimates are constructed through the parametric bootstrap approach. For the Bayesian approach, posterior inference is performed through Markov chain Monte Carlo sampling with under appropriate gamma prior assumptions. To illustrate the implementation of the proposed procedures, a simulated dataset is analyzed, and a comprehensive Monte Carlo simulation study is subsequently conducted to evaluate the accuracy and efficiency of the estimators. According to the analysis, Bayesian estimators based on informative prior distributions yield more precise estimates of the CV.