On the structure of the Poisson trinomial distribution
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917327891595264 |
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| author | Broadie, Mark Petkova, Ina |
| author_facet | Broadie, Mark Petkova, Ina |
| contents | We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the half-integers. Each part, when normalized, is a Poisson binomial distribution and hence log-concave with one or two modes. We also prove that each of the two conditional means (conditioning on being an integer or a half-integer) lies within $1/2$ of the unconditional mean. As a consequence, any two modes of the two conditional distributions are within $5/2$ of each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the structure of the Poisson trinomial distribution Broadie, Mark Petkova, Ina Probability We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the half-integers. Each part, when normalized, is a Poisson binomial distribution and hence log-concave with one or two modes. We also prove that each of the two conditional means (conditioning on being an integer or a half-integer) lies within $1/2$ of the unconditional mean. As a consequence, any two modes of the two conditional distributions are within $5/2$ of each other. |
| title | On the structure of the Poisson trinomial distribution |
| topic | Probability |
| url | https://arxiv.org/abs/2603.09019 |