On raw moments of the binomial distribution
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915233391443968 |
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| author | Leppälä, Kalle |
| author_facet | Leppälä, Kalle |
| contents | We study the $k$:th raw moment of a variable $R$ following the binomial distribution $\text{B}(n, p)$, where $n/k \rightarrow β> 0$. It is known that $\mathbb{E}(R^k)$ is bounded both from below and from above by functions of the form $k^k Ψ^k$. We solve the asymptotically optimal value of $Ψ$ as a function of $p$ and $β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On raw moments of the binomial distribution Leppälä, Kalle Probability 60C05, 05A16, 11B73 G.3; G.2.1 We study the $k$:th raw moment of a variable $R$ following the binomial distribution $\text{B}(n, p)$, where $n/k \rightarrow β> 0$. It is known that $\mathbb{E}(R^k)$ is bounded both from below and from above by functions of the form $k^k Ψ^k$. We solve the asymptotically optimal value of $Ψ$ as a function of $p$ and $β$. |
| title | On raw moments of the binomial distribution |
| topic | Probability 60C05, 05A16, 11B73 G.3; G.2.1 |
| url | https://arxiv.org/abs/2504.05766 |