Example of a parametric family of distributions that always has dependence on among its variables

Asked Dec 07 '21 at 03:22

Active Dec 07 '21 at 03:22

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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?

asked Dec 07 '21 at 03:22

DifferentialPleiometry

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Let $X, Y$ satisfy $X^2 + Y^2 =1$. Whatever joint you define, $X, Y$ will be dependent. – kjetil b halvorsen Dec 07 '21 at 03:29
@kjetilbhalvorsen Ah yes, an equality constraint! Very good example. – DifferentialPleiometry Dec 07 '21 at 03:32

Example of a parametric family of distributions that always has dependence on among its variables

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