The first negative moment of skew-t and generalized student's t -distributions in the principal value sense

The (cauchy) principal value is a method for assigning values to certain improper integrals which would otherwise be undefined. using the principal value sense,this study derives an explicit expression of the first negative moment of skew-t and generalized student's t-distributions for practical applications. some applications obtained from the fnm of skew-t and generalized student's t-distributions are also discussed. © 2013 chien-yu peng.