Bayesian and non-bayesian estimation of Marshall-Olkin XLindley distribution in presence of censoring, cure fraction, and application on medical data

In this study, a new two-parameter Marshall Olkin XLindley (MOXL) distribution is proposed and investigated. We determine important statistical characteristics of the MOXL distribution, such as its quantile function, reliability metrics, moments, and other measures. We also characterize the new model based on truncated moments and the hazard rate function. We estimate the parameters of the distribution using both maximum likelihood and Bayesian approaches. We employ three medical datasets to show the MOXL distribution's adaptability. The MOXL distribution produces more efficient outcomes than other widely used probability models. We also use Bayesian analysis using a gamma prior to estimating parameter values.