A study on the $F$-distribution motivated by ChvÃ¡tal's theorem

Qianqian Zhou; Peng Lu; Zechun Hu

paper

A study on the $F$ -distribution motivated by ChvÃ¡tal's theorem

arXiv:2409.09420

Abstract

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 $I^º > 0,$ we investigate the infimum value of the probability $P (X_{d_{1}, d_{2}} \leq I^º E [X_{d_{1}, d_{2}}])$ . Our motivation comes from ChvÃ¡tal's theorem on the binomial distribution.

A study on the F-distribution motivated by ChvÃ¡tal's theorem

Abstract

A study on the $F$ -distribution motivated by ChvÃ¡tal's theorem