Abstract
Let G p denote the tail function of Student’s distribution with p degrees of freedom. It is shown that the ratio G q (x)/G p (x) is decreasing in x > 0 for any p and q such that 0 < p < q ≤ ∞. Therefore, G q (x) < G p (x) for all such p and q and all x > 0. Corollaries on the monotonicity of (generalized) moments and ratios thereof are also given.
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Pinelis, I. Monotone tail and moment ratio properties of Student’s family of distributions. Math. Meth. Stat. 24, 74–79 (2015). https://doi.org/10.3103/S1066530715010056
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DOI: https://doi.org/10.3103/S1066530715010056