Bayesian analysis of 3-components Kumaraswamy mixture model: Quadrature method vs. Importance sampling

Abstract

This paper presents the Bayesian inference of the 3-component Kumaraswamy mixture distribution. The paper formulates the 3-component model, provides Bayesian estimates and their respective posterior risks assuming non-informative prior under type-I censoring. Since the Bayes estimates are not in closed form, the paper provides a comparative analysis of the estimates and their respective risks derived under quadrature method and importance sampling using different loss functions, assuming different sample sizes, test termination times and mixture probabilities. Finally, the proposed 3 component mixture model is then applied to the real life data to assess its validity. The convergence of the estimates under importance sampling is rapidly observed as compared to quadrature methods.