Suggested Parametrizations

A lot of distributions have reparametrizations of the form μ, ν where μ is the mean or scale, while ν represents the degrees of freedom. Examples are the Beta distribution written in terms of `μ=α/(α+β)` and `ν=α+β`, or the inverse gamma rewritten as the scaled inverse chi squared distribution (and similarly for gamma -> scaled chi squared distribution).

Another kind of reparametrization that would be extremely useful are the orthogonal parametrizations. In some cases, it's possible to rewrite a distribution of several variables as the product of two distributions, each of which only depends on one of the parameters. For instance, the gamma distribution [can be rewritten in terms of the log of the geometric mean and the log of a scale parameter](https://discourse.mc-stan.org/t/posterior-estimates-of-rate-and-shape-of-gamma-distribution-are-dependent/3220/2). Orthogonal parametrizations can help speed up some inference algorithms, can make setting priors or building models easier, and can help with communicating/visualizing/interpreting models by providing parameters that are independent (or approximately so).