A monotonicity property of variances

2012/10/16 by J. M. Aldaz, Aldaz, J. M.
Decision Sciences · Mathematics · #26D15 #60A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Probability (math.PR) #Probability and Risk Models #math.CA #math.PR #msc:26D15 #msc:60A10

paper · pdf · doi:10.48550/arxiv.1210.4417

arxiv created 2012/10/16 · openalex publication_date 2012/10/16 · arxiv updated 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that variances of non-negative random variables have the following monotonicity property: For all 0 < r < s ≤ 1, and all 0 ≤ X ∈ L², we have Var(X^r)^1/r ≤ Var(X^s)^1/s. We also discuss the real valued case.

Citations

• Sharp bounds for the difference between the arithmetic and geometric means

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