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In contrast to distribution functions, these are all implemented in pure Julia, require no external dependencies, and thus have no license issues. In fact, while they are used in statistics, they are not even "statistical" functions since other fields make ample use of them. Cf #20; these functions are useful for the end user directly, without requiring an interface like Distributions.jl.
I propose LogExpFunctions.jl as a package name. If the discussion suggests this makes sense, I would be happy to do a PR.