BAYESIAN ROBUST ANALYSIS FOR NON-NORMAL DATA BASED ON A PERTURBED-t MODEL

The article develops a new class of distributions by introducing a nonnegative perturbing function to $t_\nu$ distribution having location and scale parameters. The class is obtained by using transformations and conditioning. The class strictly includes $t_\nu$ and $skew-t_\nu$ distributions. It provides yet other models useful for selection modeling and robustness analysis. Analytic forms of the densities are obtained and distributional properties are studied. These developments are followed by an easy method for estimating the distribution by using Markov chain Monte Carlo. It is shown that the method is straightforward to specify distribution ally and to implement computationally, with output readily adopted for constructing required criterion. The method is illustrated by using a simulation study.