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

= March 10 =

Mixed Poisson Distribution
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 $$f(k) = \frac{1}{k!} \int_0^\infty x^k e^{-x}g(x) \mathrm d x$$ which is not Poisson distibuted in general. Greetings Bigbossfarin (talk) 14:35, 10 March 2022 (UTC)


 * 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 $$\pi(\lambda)=\delta(\lambda-\lambda_0),$$ in which $$\delta$$ denotes the Dirac delta function, representing a random variable with a one-point distribution. --Lambiam 16:51, 10 March 2022 (UTC)
 * Dear 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)
 * Using the variable names of, the "outer" parametrized distribution $$F$$ can always be retrieved by using a shifted Dirac delta distribution for the "inner" parameter distribution $$G$$. 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)

Mathematics using templates
How do I insert the divided value of /  into a page? Hcoder3104☭ (💬) 18:10, 10 March 2022 (UTC)
 * By using the parser functions extension #expr; see Help:Extension:ParserFunctions&thinsp;§&thinsp;#expr at Mediawiki. For example, produces . You'll need to filter out the commas first using NaN; otherwise #expr chokes on the commas. For example, while  may produce 1,071,649,631, by using 0 you get the string 1071649631.  --Lambiam 19:26, 10 March 2022 (UTC)