Copulas in squash

June 15, 2009 in Math,Sports

Somehow I never noticed this before, but the marks on the walls of the Harvard Club squash courts form excellent copula scatterplots.

Here is a picture of the court, courtesy HCNY's new website:

And here is a quick simulation I just ran of 10,000 points drawn from a Clayton copula with theta = 1.25:

Clayton copula scatterplot (theta = 1.25)

It's not perfect, but it's pretty close. To fully match the pictured relationship, we'd need to assume the correct marginal distributions as well. Of course one could also make the argument that theres a more complex dependence structure at work here, given the strong diagonal band in the wall markings. Dare I plug the Fourier copula as a more  appropriate tool?

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