Heterogeneous data analysis using a mixture of Laplace models with conjugate priors

The development of flexible parametric classes of probability models in Bayesian analysis is a very popular approach. This study is designed for heterogeneous population for a two-component mixture of the Laplace probability distribution. When a process initially starts, the researcher expects that the failure components will be very high but after some improvement/inspection it is assumed that the failure components will decrease sufficiently. That is why in such situation the Laplace model is more suitable as compared to the normal distribution due to its fatter tails behaviour. We considered the derivation of the posterior distribution for censored data assuming different conjugate informative priors. Various kinds of loss functions are used to derive these Bayes estimators and their posterior risks. A method of elicitation of hyperparameter is discussed based on a prior predictive approach. The results are also compared with the non-informative priors. To examine the performance of these estimators we have evaluated their properties for different sample sizes, censoring rates and proportions of the component of the mixture through the simulation study. To highlight the practical significance we have included an illustrative application example based on real-life mixture data.