Factorial Moments of the Geometric Distribution of Order $k$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914625698660352 |
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| author | Mane, S. R. |
| author_facet | Mane, S. R. |
| contents | We derive a simple expression for the $r^{th}$ factorial moment $μ_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically, $μ_{(r)} = r!f_k((r+1)k+r)/((qp^k)^{r+1})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15886 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Factorial Moments of the Geometric Distribution of Order $k$ Mane, S. R. Probability Combinatorics 60E05, 39B05, 11B37, 05-08 We derive a simple expression for the $r^{th}$ factorial moment $μ_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically, $μ_{(r)} = r!f_k((r+1)k+r)/((qp^k)^{r+1})$. |
| title | Factorial Moments of the Geometric Distribution of Order $k$ |
| topic | Probability Combinatorics 60E05, 39B05, 11B37, 05-08 |
| url | https://arxiv.org/abs/2312.15886 |