Limiting distributions of ratios of Binomial random variables

Adriel Barretto; Zachary Lubberts

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arXiv · 2506.13071

Limiting distributions of ratios of Binomial random variables

Adriel Barretto·Zachary Lubberts

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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.

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Adriel Barretto, Zachary Lubberts. 2025-06-16. Limiting distributions of ratios of Binomial random variables. https://arxiv.org/abs/2506.13071

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