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Adding a section on the CDF

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Would it make sense to add a subsection for the CDF under the definitions, like there is for the Binomial distribution? FynnFreyer (talk) 19:07, 21 November 2023 (UTC)[reply]

Modelled after the linked section it could look like this:
The cumulative distribution function can be expressed as:
where is the "floor" under k, i.e. the greatest integer less than or equal to k, and is the factorial function.
It can also be represented in terms of the upper incomplete gamma function or the regularized gamma function , as follows:
[1]
FynnFreyer (talk) 19:24, 21 November 2023 (UTC)[reply]

References

  1. ^ Other, Someone Or (1234). TODO: find proper citation. Place: Publisher. p. 1.


Other Properties - Mitzenmacher

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Source does not support this statement in the article:

and 

See https://imgur.com/a/3lE0VDa

2A02:1811:351E:AF00:2966:4372:24C8:154B (talk) — Preceding undated comment added 23:58, 12 January 2024 (UTC)[reply]

You are right: there is a typo in the source. However the statement on Wikipedia is correct:
Value of Numerical approx.
1 2/e 0.73575...
2 5/e2 0.67667...
3 13/e3 0.64723...
4 0.62883...
5 0.61596...
More values can be obtained, e.g, with the following Python function
f = lambda n : sum(n**k * math.exp(-n) / math.factorial(k) for k in range(n + 1))
(note that this is poorly implemented, and that it overflows for μ ≥ 144).
In view of this, it's pretty clear that the mistake in the source is a typo rather than an actual mathematical error. Still, it's a problem... Especially since I wouldn't know where to find a source for this kind of statement. It's not too hard to see that the statement should be true for large (e.g, because the variables can be coupled in such a way that is a random walk whose increments are centered and have variance 1), but even if someone provides a proof here, it might be considered original research.
As far as I'm concerned:
  • the fact that there is a mistake is not a huge problem, since it's clearly a typo; but I understand that some people might disagree;
  • the fact that there is no proof in the source is a bigger problem;
  • I think the statement is cool, but it's relevance is actually not so clear.
Malparti (talk) 18:57, 13 January 2024 (UTC)[reply]

Add a simple introduction

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This article is hard to read unless you already know what a Poisson distribution is, and that is unnecessary.

It would help to start out with a simple introduction of the term Poisson_process. Perhaps add an illustration to help the reader. Subsequently use this section to define the Poisson distribution. — Preceding unsigned comment added by 89.23.239.207 (talk) 13:28, 23 September 2024 (UTC)[reply]