Moments of Student's t-distribution: A Unified Approach
11 Pages Posted: 18 Dec 2019 Last revised: 28 Jan 2021
Date Written: December 2, 2019
In this paper, we derive the closed form formulae for moments of Student's t-distribution in the one dimensional case as well as in higher dimensions through a unified probability framework. Interestingly, the closed form expressions for the moments of Student's t-distribution can be written in terms of the familiar Gamma function, Kummer's confluent hypergeometric function, and the hypergeometric function.
Keywords: Normal distribution, Student's t-distribution, Moment, Raw Moment, Absolute Moment, Multivariate
JEL Classification: 91G80, 93E11, 93E20
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