# Relationships among statistical distributions

Posted 9 years ago
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 When I read Diagram of distribution relationships I immediately thought of built in Wolfram Language function TransformedDistribution. That blog article features the following diagram:Many of these relationships can be verified. For example well known: TransformedDistribution[Exp[u], u \[Distributed] NormalDistribution[?, ?]] LogNormalDistribution[?, ?]or less known TransformedDistribution[(u/n)/(v/m), {u \[Distributed] ChiSquareDistribution[n], v \[Distributed] ChiSquareDistribution[m]}] FRatioDistribution[n, m]But not only we could verify the diagram, but also discover numerous other relationships. From simple ExponentialDistribution:to exotic: TransformedDistribution[Sqrt[x^2 + y^2], {x, y} \[Distributed] BinormalDistribution[{a, b}, {c, d}, e]] BeckmannDistribution[a, b, c, d, e]When Mathematica 8 came out we already had largest distribution support:and as you can see fundamental symbolic nature of Wolfram Language allows to go much beyond simple formula listings. As further reading I recommend the blog post The Ultimate Univariate Probability Distribution Explorer.