After discussing this on Slack with @kellertuer, we realized most of these cases can be realized as special cases of a few generic distributions we can define on arbitrary manifolds. This motivated this issue to get these implemented directly in Manifolds.jl: https://github.com/JuliaNLSolvers/Manifolds.jl/issues/57. It might still be worth it to have a special package that wraps these generic distributions for easier use and includes some special functions for e.g. MLE.
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