The distribution should be obtainable by integrating over the section of the simplex segment of the surface of the hypersphere bounded by the points (1,0,0,0,...), (1,1,0,0,0...)/sqrt(2), (1,1,1,0,0...)/sqrt(3) etc. along the ith axis.
All the distributions (n,m) have support contained within the unit interval, are piecewise smooth and share the same set of non-smooth points at the reciprocals of the square roots of the natural numbers.
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