Bayesian Analysis of 3-Component Unit Lindley Mixture Model with Application to Extreme Observations

Bayesian inference of the 3-component unit Lindley right censored mixture is presented in this paper. The posterior distributions of the parameters are derived assuming informative (gamma) as well as noninformative (uniform and Jeffreys) priors. For the gamma (informative) prior, hyperparameters are elicited using prior predictive distribution. The Bayesian estimation has been carried out considering both symmetric and asymmetric loss functions (squared error, quadratic, weighted, and precautionary loss functions). Simulation studies for various sample sizes and different threshold values (test termination times) are considered to evaluate the performances of the Bayes estimators w.r.t their posterior risks under the said loss functions. Real life flood data from Naser Lake is also analyzed as a 3-component mixture for the sake of illustrative purpose. The simulation study and data analysis reveals that the estimates under informative prior perform better than the noninformative priors. Also, it is observed that the increase in sample size and the threshold value (test termination time) are inversely proportional to the posterior risks. Among the loss functions considered, the loss functions performance from the best to the least, w.r.t the posterior risk, is as follows: precautionary loss function