Automatic reparametrizations of distributions in Distributions.jl

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Hi everyone,

I’m thinking about a potential feature for the Distributions.jl package that would be nice to have. Would it be possible to implement a function, let’s say reparametrize, that takes an existing distribution and a parameter transformation function to create a new distribution object?

For example, a common reparametrization is moving from the standard deviation to precision. We could define a transformation for a Normal(μ, σ) distribution to a new version parametrized by τ = 1/σ².

This would streamline our workflow and reduce the need for writing custom distribution types for common transformations. It feels like a powerful tool for building flexible statistical models.

What do you all think? Is this concept feasible, and has anything like it been proposed or implemented before?

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What interface do you need for these reparametrizations? Eg, would adding a precision(d::Normal) = 1/σ^2 function would be enough?