Classical and Bayesian Estimation for the Parameters of a Competing Risk Model Based on Minimum of Exponential and Gamma Failures

The paper provides both classical and Bayesian estimation of the parameters of a competing risk model defined on the basis of minimum of exponential and gamma failure modes. Usually such situations are the examples of incomplete specification of data that naturally opens the way to expectation maximization algorithm for obtaining maximum likelihood estimates of model parameters. This incomplete specification of the data simultaneously explores the possibility of sampling importance resampling strategy with intermediate Markov chain Monte Carlo steps for the Bayesian estimation of parameters. Although this paper focuses primarily on estimation of model parameters, other inferential developments can be routinely done. Numerical illustration is provided based on both simulated and real-data examples.