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

2019/12/03 by J. Lars Kirkby, Kirkby, J. Lars, Dang Khoa Nguyen +3 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1912.01607

openalex publication_date 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, 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.

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