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LeBron James has averaged 27 pts, 7 rebounds, and 7 assists per game essentially since his debut in 2003. Despite this, he has never had a game with a stat line of exactly 27/7/7.

I'm interested in calculating the joint probability $P(Pts = 27, Reb = 7, Ast = 7)$. I had thought to model these as Poisson RVs. However, I can't find anything that describes how to estimate the covariance matrix of a multivariate Poisson vector when the components have a dependence structure.

I could just model each variable as normal, but that wouldn't be as accurate, I don't think. Let me know what you think!

RYAN ANDERSON
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  • What dependence structure do you have in mind? // For one (perhaps the simplest) way to model dependencies among Poisson variables, see https://stats.stackexchange.com/questions/108705. It generalizes in the obvious way to as many variables as you like. // If you're going to estimate a covariance matrix, you will need the multivariate data. Why not model the full distribution? – whuber Mar 13 '24 at 20:29
  • I've seen that bivariate model before, but confused as to why you would model as as sharing a common sub-process. Would be fine to model the full distribution. Another way to ask my question would be how do I find the MLE of the covar matrix for Poisson vector – RYAN ANDERSON Mar 13 '24 at 20:45
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    To find the MLE you need an explicit, parameterized model for the covariance matrix. – whuber Mar 13 '24 at 20:50
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    There are several non-equivalent ways to represent a multivariate Poisson distribution, and it will matter which one you choose, both from the point of view of parameterization of the covariance matrix and finding the MLE of the parameters of the joint distribution. – jbowman Mar 13 '24 at 21:23

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