Jump to content

Wikipedia:Reference desk/Archives/Mathematics/2022 March 10

From Wikipedia, the free encyclopedia
Mathematics desk
< March 9 << Feb | March | Apr >> Current desk >
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.


March 10

[edit]

Mixed Poisson Distribution

[edit]

In the German article for Mixed Poisson Distribution (see e.g. here) states:

The Mixed Poisson Distribution is a generalization of the Poisson Distribution.

I cannot see why this should be true. The PMF of a Mixed Poisson Distribution with PDF g(x) is which is not Poisson distibuted in general. Greetings Bigbossfarin (talk) 14:35, 10 March 2022 (UTC)[reply]

The English article Mixed Poisson distribution states the same, so I do not get why you are referring to the German Wikipedia. We have an article named Compound probability distribution, which is another term for mixed distribution – although some authors make a somewhat trivial distinction. In general, the compound distribution obtained from composing a distribution of type X and a distribution of type Y is itself of neither of the two types. The mixed Poisson distribution is called a generalization of the usual Poisson distribution because the latter can be retrieved from the former as a special case, namely by choosing in which denotes the Dirac delta function, representing a random variable with a one-point distribution.  --Lambiam 16:51, 10 March 2022 (UTC)[reply]
Dear @Lambiam: I was writing the English article a few hours ago, and I was already guessing, that there could be a way with Dirac delta. I will think about it. Greetings Bigbossfarin (talk) 18:37, 10 March 2022 (UTC)[reply]
Using the variable names of Compound probability distribution § Definition, the "outer" parametrized distribution can always be retrieved by using a shifted Dirac delta distribution for the "inner" parameter distribution . So the fact that this mixed Poisson distribution is "a generalization" of the Poisson distribution is not an interesting observation. I see we also have an article with the title Compound Poisson distribution, in which it is the "inner" parameter distribution that is Poisson.  --Lambiam 07:15, 11 March 2022 (UTC)[reply]

Mathematics using templates

[edit]

How do I insert the divided value of {{NUMBEROFEDITS}} / {{NUMBEROFACTIVEUSERS}} into a page? Hcoder3104☭ (💬) 18:10, 10 March 2022 (UTC)[reply]

By using the parser functions extension #expr; see Help:Extension:ParserFunctions § #expr at Mediawiki. For example, {{#expr:10/7 round 5}} produces 1.42857. You'll need to filter out the commas first using {{formatnum:...|R}}; otherwise #expr chokes on the commas. For example, while {{NUMBEROFEDITS}} may produce 1,071,649,631, by using {{formatnum:{{NUMBEROFEDITS}}|R}} you get the string 1071649631.  --Lambiam 19:26, 10 March 2022 (UTC)[reply]