Monotone tail and moment ratio properties of Student's family of distributions
Abstract
Let Gp denote the tail function of Student's distribution with p degrees of freedom. It is shown that the ratio Gq(x)/Gp(x) is decreasing in x>0 for any p and q such that 0<p<q∞. Therefore, Gq(x)<Gp(x) for all such p and q and all x>0. Corollaries on the monotonicity of (generalized) moments and ratios thereof are also given.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.