Analysis of the Truncated XLindley Distribution Using Bayesian Robustness

In this work, we present a robust examination of the Bayesian estimators utilizing the two-parameter Upper truncated XLindley model, a unique Lindley model variant, and the oscillation of posterior risks. We provide the model in a censored scheme along with its likelihood function. The topic of sensitivity and robustness analysis of the Bayesian estimators was only covered by a small number of authors. As a result, very few apps have been created in this field. The oscillation of the posterior hazards of the Bayesian estimator is used to illustrate the method. By using a Monte Carlo simulation study, we show that, with the correct generalized loss function, a robust Bayesian estimator of the parameters corresponding to the smallest oscillation of the posterior risks may be obtained; robust estimators can be obtained when the parameter space is low-dimensional. The robustness and precision of Bayesian parameter estimation can be enhanced in regimes where the parameters of interest are of small magnitude.