Copulas and discrete random variables

[jeffpollock9]

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I've been following Copulas Primer which constructs a bivariate distribution using Kumaraswamy and Gumbel marginals, with the copula inducing correlation between the two.

This seems possible since there is tfb.KumaraswamyCDF and tfb.GumbelCDF bijectors which transform samples from [0, 1]^2 -> R^2. There aren't however any such CDF bijectors for discrete distributions, e.g. tfd.Poisson, which makes sense since the CDF is a step function.

My question is - is there any simple way to code up bivariate distributions using copulas with discrete random variables in TFP? I know there might be some issues with copulas and discrete outcomes, but it'd be great to have a play around if possible.

Thanks!

[sanket-kamthe]

Saw this really late but I had paper on this very topic please have a look at https://arxiv.org/abs/2101.00598.

Section 4.1 and 4.2 is what you were looking for!

[jeffpollock9]

@sanket-kamthe thanks for this! I look forward to studying that in the next week or so when I can!