POSTERIOR ANALYSIS OF A COMPETING RISK MODEL BASED ON DECREASING FAILURE RATE WEIBULL AND EXPONENTIAL FAILURES

Abstract

The paper considers a competing risk model based on decreasing failure rate Weibull and constant failure rate exponential models. The failure may arise due to either of the two causes where the former represents death due to birth defect and the latter represents an accidental failure that may occur at any moment during the normal life cycle. The Bayes analysis is done using weak but proper priors for the parameters. Since the posterior analysis involves analytically intractable integrals, the paper proposes a Gibbs-Metropolis hybridization scheme to draw the corresponding posterior samples. For initial values of model parameters, the paper proposes the use of maximum likleihood estimates obtained using expectation-maximization algorithm. The numerical illustration is provided based on a simulated data example.