paper

Variation comparison between the $F$ -distribution and the normal distribution

arXiv:2305.13615

Abstract

Let $X_{d_{1}, d_{2}}$ be an $F$ -random variable with numerator and denominator degrees of freedom $d_{1}$ and $d_{2}$ , respectively. We investigate the inequality: $P {∣ X_{d_{1}, d_{2}} - E [X_{d_{1}, d_{2}}] ∣ \leq Var (X_{d_{1}, d_{2}})} \geq P {∣ W - E [W] ∣ \leq Var (W)}$ , where $W$ is a standard normal random variable or a $I ¨ ^{2} (d_{1})$ random variable. We prove that this inequality holds for $d_{1} \in {1, 2, 3, 4}$ and $5 \leq d_{2} \in N$ .

Variation comparison between the F-distribution and the normal distribution

Abstract

Variation comparison between the $F$ -distribution and the normal distribution