Timeline for Choose right pdf for lightning strike simplification [Exercice Question]
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| Sep 7, 2021 at 15:04 | comment | added | Scortchi♦ | Well $X_i \sim \mathsf{Pois}(\lambda)$ is indeed a natural, reasonable model for lightning strikes in a section (& $\sum_{i=1}^{300} X_i = N \sim \mathsf{Pois}(300\lambda)$ for lightning strikes in the entire area). But once we know the no. of strikes in the entire area the relevant distribution derived from this very model is the conditional one $X_i|N=213\sim \mathsf{Binom}\left(213, \frac{1}{300}\right)$. See stats.stackexchange.com/q/540612/17230. | |
| Sep 7, 2021 at 7:12 | comment | added | BruceET | Yes, both are reasonable. Depending on parameters, the binomial and Poisson are not always in such close agreement. The Poisson model is especially appropriate when it is not clear what binomial $n$ should be. | |
| Sep 7, 2021 at 7:07 | history | edited | BruceET | CC BY-SA 4.0 |
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| Sep 7, 2021 at 6:23 | comment | added | Wolfmercury | Thanks for the detailed answer. It kind of surprises me, that the Poisson distr. has the same accuracy to the third decimal place as the binomial, but that shows my naivety with statistics. Thanks for this insight. In my opinion then both approaches should be a reasonable answer. | |
| Sep 7, 2021 at 2:44 | history | edited | BruceET | CC BY-SA 4.0 |
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| Sep 7, 2021 at 2:33 | history | answered | BruceET | CC BY-SA 4.0 |