Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.13071 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908408637030400 |
|---|---|
| author | Barretto, Adriel Lubberts, Zachary |
| author_facet | Barretto, Adriel Lubberts, Zachary |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limiting distributions of ratios of Binomial random variables Barretto, Adriel Lubberts, Zachary Statistics Theory Probability 6E20 (Primary) 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. |
| title | Limiting distributions of ratios of Binomial random variables |
| topic | Statistics Theory Probability 6E20 (Primary) |
| url | https://arxiv.org/abs/2506.13071 |