On Bayesian Probit Modeling Of Generalized Asymmetric Student-t Distribution With Application

In financial markets, usually assume financial data obey the normal distribution. But in fact, a lot of financial data often follow leptokurtic heavy tail feature, which does not follow the normal feature. The generalized asymmetric student-t distribution(GAST) has the properties of fat tails and skewness, which can better apply in the financial market model. In this paper, we study the generalized asymmetric student-t distribution with application to the Probit model. At the same time we mainly studied the Bayesian estimation of GAST, giving the corresponding likelihood function and the prior function. Then we deduce the form of posterior. How the sampling of complex posterior density function is the key to the subject. This paper explores the Gibbs sampling for each parameter’s conditional probability, and gives the theoretical derivation of the formula. We generate simulation data of GAST by R, and use the Bayesian posterior estimation methods for parameter estimation. At last, we apply it to the prediction of corporate bankruptcy, including the selection of indicators, data processing, model building, parameter estimation and model evaluation.