Bayesian and non-bayesian approaches for estimating the Epanechnikov-Weibull distribution with applications in...

Statistical models are widely acknowledged as effective in representing practical scenarios. Nevertheless, it is imperative to recognize that they can sometimes prevent optimal fitting in certain cases. As a result of this awareness, researchers have investigated improved and more efficient probability distributions. This study examines the generalized order statistics (GOSs) of the Epanechnikov-Weibull distribution (EpWD). Statistical features, such as the moment-generating function, the rth L-moment, and trimmed L-moments for this model, are derived. Furthermore, we construct estimation techniques for the model parameters employing maximum likelihood estimation (MLE) and Bayesian approaches. Asymptotic confidence intervals (CIs) are formulated by obtaining explicit formulations for the Fisher information matrix (FIM). A Monte Carlo simulation is conducted to assess the efficacy of the suggested estimators using progressively type-II censored samples. This distribution is also analyzed for its extropy and weighted extropy as information-theoretic measures. The practical applicability of the theoretical findings is illustrated through numerical examples that utilize electronic and engineering datasets.