Limiting distributions of ratios of Binomial random variables

2025/06/16 by Adriel Barretto, Barretto, Adriel, Zachary Lubberts +1
Computer Science · Decision Sciences · Mathematics · #6E20 (Primary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2506.13071

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We consider the limiting distribution of the quantity X^s/(X+Y)^r, where X and Y are two independent Binomial random variables with a common success probability and a number of trials n and m, respectively, and r,s are positive real numbers. Under several settings, we prove that this converges to a Normal distribution with a given mean and variance, and demonstrate these theoretical results through simulations.

Citations

• Random line graphs and edge-attributed network inference

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