Timeline for Validity of Approximating a Poisson Mixture with a Simple Poisson
Current License: CC BY-SA 4.0
7 events
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| 12 hours ago | comment | added | user1420303 | @Ben Thanks. In my case, the instantaneous rate of events (λ) is influenced by many factors that change rapidly over time. I don't have a precise model for these dynamics, but I know they lead to fluctuations in λ. I'm exploring whether a simple Poisson with a constant rate (equal to the time-averaged mean of λ) can be a valid approximation. My main concern is whether the frequency of fluctuations in λ, relative to the time between events, affects the accuracy of this approximation, even if there are many fluctuations overall. I've edited the question to better reflect this. | |
| 12 hours ago | history | edited | user1420303 | CC BY-SA 4.0 |
clarifications
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| 20 hours ago | comment | added | Ben | This is unclear. Are you saying that the rate parameters for the mixture parts vary over time? If so, are you likewise updating your approximation over time? | |
| yesterday | comment | added | kjetil b halvorsen♦ | For a better probability of a useful answer, please include those motivations as an edit to the post (only as a comment as ofnow very few people will see it) | |
| yesterday | comment | added | user1420303 | @kjetilbhalvorsen Thank you very much for your suggestion. Approximating with a negative binomial distribution might indeed be more accurate in terms of capturing the increased variance. However, my primary interest lies in understanding, at a conceptual level (I'm not a mathematician), the effect (if any) that the timescale of fluctuations in λ has on the validity of the simple Poisson approximation. This is because I'm trying to connect the statistical model to an underlying physical process where the rate parameter is influenced by external factors that change over time. | |
| yesterday | comment | added | kjetil b halvorsen♦ | A Poisson mixture will have larger variance, maybe netter to approximate with a negative binomial? | |
| yesterday | history | asked | user1420303 | CC BY-SA 4.0 |