Talk:Poisson distribution

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The above message was substituted from {{IEP assignment}} by PrimeBOT (talk) on 19:54, 1 February 2023 (UTC)

Ceiling function

The same way the symbols used for the floor function are explained (in the Infobox-cdf), shouldn't the symbols for the ceiling function be also defined (appear in the "Infobox-mode" of the function)? 193.136.147.158 (talk) 13:48, 23 October 2023 (UTC)

Adding a section on the CDF

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)

Modelled after the linked section it could look like this:

The cumulative distribution function can be expressed as:

$F(k;\lambda )=\Pr(X\leq k)=e^{-\lambda }\sum _{i=0}^{\lfloor k\rfloor }{\frac {\lambda ^{i}}{i!}},$

where $\lfloor k\rfloor$ 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 $\Gamma$ or the regularized gamma function $Q$, as follows:

$F(k;\lambda )={\frac {\Gamma (\lfloor k+1\rfloor ,\lambda }{\lfloor k\rfloor !}}=Q(\lfloor k+1\rfloor ,\lambda ).$

FynnFreyer (talk) 19:24, 21 November 2023 (UTC)

References

Other Properties - Mitzenmacher

Source does not support this statement in the article:

and $\Pr(Y\leq E[Y])\geq {\frac {1}{2}}.$

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

2A02:1811:351E:AF00:2966:4372:24C8:154B (talk)