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Inspired by this question, I would like an example of a parametric family of distributions such that there is dependence for all choices of parameters. The family could be infinite or finite, but I would like the support to be infinite.

Can such an example be constructed?

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  • $\begingroup$ Let $X, Y$ satisfy $X^2 + Y^2 =1$. Whatever joint you define, $X, Y$ will be dependent. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Dec 7, 2021 at 3:29
  • $\begingroup$ @kjetilbhalvorsen Ah yes, an equality constraint! Very good example. $\endgroup$
    – Galen
    Commented Dec 7, 2021 at 3:32

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