# Generating multivariate Poisson dataset

My question is what kinds of events is multivariate Poisson distributed ? I need to find or generate a dataset which has got this distribution ?

I thought of random vector $$X=(X_1 , X_2)$$ where $$X_1$$ descirbes the goal per game and $$X2$$ describes the foul per game for a football player ? But I am not sure if my $$X$$ then is multivariate poisson distributed ?

• $X2$ is unlikely to have a Poisson distribution if it's fouls per player, because those will be multiples of 1/11.
– whuber
Dec 3, 2022 at 21:36

Your solution is pretty nice. Here is another case, also in the context of soccer:

http://www2.stat-athens.aueb.gr/~karlis/multivariate%20Poisson%20models.pdf

$$X=(X_a, X_h)$$ where $$X_a$$ is the number of away goals (when playing away), and $$X_h$$ is the number of home goals (when playing at home)

Another example from same file above:

Number of crimes of each type: (rapes , arson, manslaughter, smuggling)

Karlis, D. (2003). An EM algorithm for multivariate Poisson distribution and related models. Journal of Applied Statistics, 30(1), 63-77.

• i found a really good one but not sure if the dataset is to small for my idea! i want to implement the em algoirthm with poisson mixture models and use this dataset. kaggle.com/datasets/varpit94/football-teams-rankings-stats but i am not sure what can i use for clusters? my idea was to use the tournament as the clusters ? i want to classifiy via the stats which tournamen a team belongs ? but not sure if this is a good idea ?
– heyoka955
Dec 3, 2022 at 13:49