Timeline for What is the distribution of a Poisson variable, where the Poisson rate is Normal (or Binomial)?
Current License: CC BY-SA 3.0
17 events
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| Nov 12, 2020 at 23:06 | answer | added | Sextus Empiricus | timeline score: 1 | |
| May 2, 2020 at 9:43 | history | edited | Stephan Kolassa |
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| Jan 12, 2020 at 18:07 | answer | added | kjetil b halvorsen♦ | timeline score: 3 | |
| Jan 12, 2020 at 18:06 | history | edited | kjetil b halvorsen♦ |
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| Nov 22, 2017 at 4:28 | history | tweeted | twitter.com/StackStats/status/933190413879349248 | ||
| Nov 21, 2017 at 22:00 | comment | added | Zahava Kor | @Ian Sudbery - Poisson X with Poisson lambda is still Poisson right? - wrong. For Poisson, lambda has to be a constant, cannot have any distribution. | |
| Nov 21, 2017 at 18:17 | comment | added | Stephan Kolassa | Regarding the negbin: On the one hand, I personally am good with "because it works". On the other hand, Hilbe's Negative Binomial Regression lists many, many motivations and constructions that all lead to the negbin. (But that doesn't have much to do with your original question, which I find interesting and wait for an answer on.) | |
| Nov 21, 2017 at 16:52 | comment | added | Ian Sudbery | The claim doing the rounds is that using the NB for counts (or equivalently Gamma for the distribution of concentrations) is an empirical decision without a mechanistic model to justify it. | |
| Nov 21, 2017 at 14:55 | comment | added | Stephan Kolassa | "But why gamma": the gamma is positive, so it's a parameterization of $\lambda$ that makes more sense than a normal distribution. And of course another rationale for the gamma is that the resulting negative binomial is at least somewhat tractable. | |
| Nov 21, 2017 at 14:44 | comment | added | Xi'an | A Poisson parameter $\lambda$ cannot be negative hence cannot be Normal. | |
| Nov 21, 2017 at 14:41 | comment | added | Ian Sudbery | @Bernhard: Interesting, I hadn't thought of that. I was think of the fact that large n Binomial is approximately Gaussian. Under what circumstances do we think of large n Binomial as normal, and what circumstances Poisson? Poisson X with Poisson lambda is still Poisson right? Interestingly this doesn't fit the data. | |
| Nov 21, 2017 at 14:31 | history | edited | wolfies | CC BY-SA 3.0 |
fixed title and some typesetting
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| Nov 21, 2017 at 14:21 | comment | added | Bernhard | You write "A model that we are more used to might be [...] binomially distributed with large n)": And that is Poisson. Citing from Wikipedia for simplicity: "The Poisson distribution can be derived as a limiting case to the binomial distribution as the number of trials goes to infinity and the expected number of successes remains fixed" or en.wikipedia.org/wiki/Poisson_distribution#law_of_rare_events . Binomial and Poisson are always positive. | |
| Nov 21, 2017 at 14:14 | comment | added | Taylor | @wolfies it stands for "too long; didn't read." | |
| Nov 21, 2017 at 13:42 | comment | added | wolfies | 1. The Poission $\lambda$ parameter is required to be positive, so some care is needed if you want to assume that $\lambda$ is Normal, to ensure the Normail tails do not practically become negative. _______ 2. One can solve the parameter-mix distribution for your desired Poisson-Normal as a closed form, but it is a bit messy with Hypergeometric1F1 functions. ___3. What is the meaning of your title: TL:DR? | |
| Nov 21, 2017 at 12:30 | history | edited | Ferdi | CC BY-SA 3.0 |
deleted 2 characters in body; edited tags
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| Nov 21, 2017 at 12:29 | history | asked | Ian Sudbery | CC BY-SA 3.0 |