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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 ?

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

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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.

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  • $\begingroup$ 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 ? $\endgroup$
    – heyoka955
    Dec 3, 2022 at 13:49

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