由 Chvátal 定理引发的 F$ 分布研究

arXiv - MATH - Probability Pub Date : 2024-09-14 DOI:arxiv-2409.09420

Qianqian Zhou, Peng Lu, Zechun Hu

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引用次数: 0

摘要

假设 $X_{d_1, d_2}$ 是一个 $F$ 随机变量，参数为 $d_1$ 和 $d_2，期望为 $E[X_{d_1,d_2}]$。在本文中，对于任意 $\kappa>0,$ 我们将研究概率 $P(X_{d_1, d_2}\leq \kappaE[X_{d_1, d_2}])$ 的下限值。我们的动机来自于 Chv\'{a}tal 关于二项式分布的定理。

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A study on the $F$-distribution motivated by Chvátal's theorem

Let $X_{d_1, d_2}$ be an $F$-random variable with parameters $d_1$ and $d_2,$ and expectation $E[X_{d_1, d_2}]$. In this paper, for any $\kappa>0,$ we investigate the infimum value of the probability $P(X_{d_1, d_2}\leq \kappa E[X_{d_1, d_2}])$. Our motivation comes from Chv\'{a}tal's theorem on the binomial distribution.

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arXiv - MATH - Probability

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