An integral over $(0,π)$ for the distribution function of a sum of independent gamma random variables and for quadratic forms of Gaussian variables
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916528939597824 |
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| author | Royen, Thomas |
| author_facet | Royen, Thomas |
| contents | An integral over the interval $(0,π)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite quadratic form is obtained as a special case with identical shape parameters $α= 1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An integral over $(0,π)$ for the distribution function of a sum of independent gamma random variables and for quadratic forms of Gaussian variables Royen, Thomas Probability 62E15, 60G50 An integral over the interval $(0,π)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite quadratic form is obtained as a special case with identical shape parameters $α= 1/2$. |
| title | An integral over $(0,π)$ for the distribution function of a sum of independent gamma random variables and for quadratic forms of Gaussian variables |
| topic | Probability 62E15, 60G50 |
| url | https://arxiv.org/abs/2412.12937 |