Moments of Student's t-distribution: A Unified Approach

11 Pages Posted: 18 Dec 2019 Last revised: 28 Jan 2021

See all articles by Justin Kirkby

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Dang Nguyen

University of Alabama

Duy Nguyen

Marist College - Department of Mathematics

Date Written: December 2, 2019

Abstract

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

Suggested Citation

Kirkby, Justin and Nguyen, Dang and Nguyen, Duy, Moments of Student's t-distribution: A Unified Approach (December 2, 2019). Available at SSRN: https://ssrn.com/abstract=3497188 or http://dx.doi.org/10.2139/ssrn.3497188

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

Dang Nguyen

University of Alabama ( email )

Box 870224
200 Alston Hall
Tuscaloosa, AL 35487
United States

Duy Nguyen (Contact Author)

Marist College - Department of Mathematics ( email )

NY
United States

HOME PAGE: http://sites.google.com/site/nducduy/

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