I'd like to point out another (related) thing though that is wrong with the state of statistics in Julia, in my opinion. Actually my problem has less to do with statistics, per se, than the mathematical foundations of statistical calculations. There are, of course, many different approaches to statistical inference (the Bayesian vs. frequentist camps infamous among these), but the calculations all come down to reasoning about probabilities which is a well posed but not always easy task. The Julia developers, in their wisdom, have recognized this, and as such have put together Distributions.jl the purpose of which is to provide datatypes and utility functions over probability distributions (plus some vestigial methods about maximum likelihood inference, which thankfully stay out of the way). If you haven't seen it, check it out. It's got a nice design, I think.
But there is presently a clear server limitation: the parameterized type hierarchy. The requirement is that every distribution have support over a set in which all members are either Univariate, Multivariate or Matrixvariate with elements in the fields being either Discrete or Continuous. This obviously misses the general picture of the kinds of sets from which one draws random variables, which plays into issues that the article mentions (if the probability distribution datatype can't model the data you have to do ad hoc things to account for it). Indeed a huge chunk of the issues currently open in the Distributions github page essential boil down to problems with representing the sets and/or spaces from which elements in the distribution are drawn:
https://github.com/JuliaStats/Distributions.jl/issues/147 https://github.com/JuliaStats/Distributions.jl/issues/309 https://github.com/JuliaStats/Distributions.jl/issues/224 https://github.com/JuliaStats/Distributions.jl/issues/283
End users have a variety of well developed ideas in mind about the sets that their samples belong to and even the spaces from which they are drawn from which currently exceed the representational capacity of the existing types. In my opinion the way to fix this is to start a separate library that focuses on types and methods for representing and manipulating sets and spaces (i.e. topological information attached to sets). This could then be consumed by the Distributions people as well as others modeling things outside of probability.