Preference of Prior for Two-Component Mixture of Lomax Distribution

Abstract

Recently, El-Sherpieny et al., (2020), suggested Type-II hybrid censoring method for parametric estimation of Lomax distribution (LD) without due regard being given to the choice of priors and posterior risk associated with the model. This paper fills this gap and derived the new LD model with minimum posterior risk for the selection of priors. It derives a closed form expression for Bayes estimates and posterior risks using square error loss function (SELF), weighted loss function (WLF), quadratic loss function (QLF) and DeGroot loss function (DLF). Prior predictive approach is used to elicit the hyperparameters of mixture model. Analysis of Bayes estimates and posterior risks is presented in terms of sample size n, mixing proportion p and censoring rate t0, with the help of simulation study. Usefulness of the model is demonstrated on applying it to simulated and real-life data which show promising results in terms of better estimation and risk reduction.

Keywords

• Mixture of Lomax distribution
• Censored sampling
• Elicitation of hyperparameter
• Bayes estimator
• Posterior risk
• Loss function