Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.17614 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912542437146624 |
|---|---|
| author | Townes, F. William |
| author_facet | Townes, F. William |
| contents | Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have nonnegative support. We show this assumption is unnecessary and real-valued mixing distributions are also possible. Informally, the mixing distribution merely needs to have a light (subexponential) left tail and a small amount of probability mass on negative values. We provide several concrete examples, including the mixed Poisson-extreme stable family, where the mixing distribution has a power law tail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed Poisson families with real-valued mixing distributions Townes, F. William Probability 60E05 (Primary) 62E10 (Secondary) G.3 Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have nonnegative support. We show this assumption is unnecessary and real-valued mixing distributions are also possible. Informally, the mixing distribution merely needs to have a light (subexponential) left tail and a small amount of probability mass on negative values. We provide several concrete examples, including the mixed Poisson-extreme stable family, where the mixing distribution has a power law tail. |
| title | Mixed Poisson families with real-valued mixing distributions |
| topic | Probability 60E05 (Primary) 62E10 (Secondary) G.3 |
| url | https://arxiv.org/abs/2407.17614 |