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

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arxiv 1912.01607 v3 pith:OLWC5YCX submitted 2019-12-03 math.PR math.STstat.TH

J. Lars Kirkby , Dang Nguyen , Duy Nguyen This is my paper · ORCID
classification math.PRmath.STstat.TH
keywords functionmomentsstudentt-distributionclosedformhypergeometricunified
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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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Cited by 2 Pith papers

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    gr-qc 2026-07 accept novelty 7.0 of 10

    A standardizing coordinate transform turns PTA Fourier coefficients into near-standard normals so HMC/NUTS on GPU recovers NANOGrav-scale posteriors in ~15 minutes.

  2. Efficient Fireworks Algorithm Equipped with an Explosion Mechanism based on Student's T-distribution

    cs.NE 2025-06 conditional novelty 6.0 of 10

    A fireworks algorithm that samples explosions from an adaptive Student's t-distribution matches state-of-the-art CMA-ES and DE variants on CEC2013 and CEC2017 benchmarks.

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