On bilateral selection t model and its application to inequality constrained problems

This paper proposes a class of bilateral selection t models that is associated with the centrally truncated bivariate Student-t distributions. The class, especially useful for modeling inequality constrained parameter problems, is obtained from the nontruncated marginal of the centrally truncated bivariate Student-t distributions. The class of distributions, possibly bimodal, strictly includes univariate Student-t distribution, but with extra parameters to regulate perturbation of the symmetry. A probabilistic representation of the class is also available. Utilizing the representation, variety of properties of the class are studied and the perturbation of the symmetry is investigated in terms of skewness. These developments are followed by practical applications.