DistributionsExtra.jl

Distributions.jl-related functions of general interest that cannot/unlikely to be included into Distributions.jl itself.

Current content:

• ℙ(pred, dist). Compute the probability of a predicate being true under a given distribution. In mathematical terms, it computes ℙ(pred(x)) given that x ~ dist.

  julia> ℙ(>(0), Normal(0, 1))
  0.5
  
  julia> ℙ((@o abs(_) > 2), Normal(0, 1))
  0.04550026309183032

  All calculations are analytic by default, no numerical integration involved. See more details in the ℙ docstring.
  (also suggested in a Distributions.jl PR discussion)

• Support for intervals from IntervalSets.jl whenever it makes sense (unfortunately, the corresponding PR to Distributions.jl wasn't accepted):

  • Uniform(1..5), truncated(dist, 0..Inf), ...
  • convert to/from Distributions.RealInterval custom type
  • uniform(X) function that returns the uniform distribution on X; works for intervals, ranges, and vectors of numbers

• Finally, some specialized distribution types. They are intended to only be here temporarily, and upstreamed to Distributions.jl or Manifolds.jl at some point.

  • PiecewiseUniform (Distributions.jl PR stuck for years)
  • Uniform on a sphere: SphereUniformArea for 3d xyz parametrization, and SphereUniformLonLat for 2d lon-lat parametrization (a useful distribution but the specific semantics is tricky, [1])
  • Piecewise-uniform on a sphere: SpherePiecewiseLatUniformArea for 2d lon-lat parametrization