Bayesian analysis of two-piece location–scale models under reference priors with partial information

Bayesian estimators are developed and compared with the maximum likelihood estimators for the two-piece location–scale models, which contain several well-known distributions such as the asymmetric Laplace distribution, the two-piece normal distribution, and the two-piece Student-tt distribution. For the validity of Bayesian analysis, it is essential to use priors that could lead to proper posterior distributions. Specifically, reference priors with partial information have been considered. A sufficient and necessary condition is established to guarantee the propriety of the posterior distribution under a general class of priors. The performance of the proposed approach is illustrated through extensive simulation studies and real data analysis.