The First Negative Moment of Skew-t and Generalized Student's t-Distributions in the Principal Value Sense

Abstract

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.