For 10 points, identify this probability distribution, used to model the number of low-probability events that occur in a specific time period.
The non-linear Anscombe transform on this type of variable sets the variance of it to 1, and Dobinski's formula demonstrates that nth Bell number is the nth moment of this distribution. With PDF proportional to its characteristic value to the k over k factorial, the difference between two variables with this distribution follows the Skellam distribution, and it can be considered a limiting case of the binomial distribution. It has both mean and variance lambda, and von Bortkiewicz used it to model deaths by horse kick in the Prussian army, illustrating his proposed Law of Small Numbers. For 10 points, identify this probability distribution, used to model the number of low-probability events that occur in a specific time period.
The non-linear Anscombe transform on this type of variable sets the variance of it to 1, and Dobinski's formula demonstrates that nth Bell number is the nth moment of this distribution.
Poisson Distribution