Variation comparison between the F-distribution and the normal distribution

2023/05/23 by Ping Sun, Sun, Ping, Ze-Chun Hu +3
Decision Sciences · Mathematics · #60E15 #62G32 #90C15 #FOS: Mathematics #Fuzzy Systems and Optimization #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2305.13615

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let X_d1,d2 be an F-random variable with numerator and denominator degrees of freedom d₁ and d₂, respectively. We investigate the inequality: P\|X_d1,d2-E[X_d1,d2]|≤ √\rm Var(X_d1,d2)\≥ P\|W-E[W]|≤ √\rm Var(W)\, where W is a standard normal random variable or a χ²(d₁) random variable. We prove that this inequality holds for d₁∈\1,2,3,4\ and 5≤ d₂∈ℕ.

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