Moments of Student’s t-distribution: a unified approach
Pub. online: 25 April 2025
Type: Research Article
Open Access
Open Access
Received
1 August 2024
1 August 2024
Revised
31 March 2025
31 March 2025
Accepted
31 March 2025
31 March 2025
Published
25 April 2025
25 April 2025
Abstract
In this paper, new closed form formulae for moments of the (generalized) Student’s t-distribution are derived 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 the Student’s t-distribution can be written in terms of the familiar Gamma function, Kummer’s confluent hypergeometric function, and the hypergeometric function. This work aims to provide a concise and unified treatment of the moments for this important distribution.
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