Truncated distributions not compatible with autodiff

[clint-leach]

This came up in a project I am working on:

using ForwardDiff
using Distributions

Truncated(Normal(ForwardDiff.Dual(0.0), ForwardDiff.Dual(1.0)), 0.0, Inf)

which produces a "cannot convert object of type ForwardDiff.Dual to Float64" error. The error seems to result from trying to store the cdf calculations in the Truncated struct. Locally, I fixed this with:

struct Truncated{D<:UnivariateDistribution, S<:ValueSupport, T<:Real} <: UnivariateDistribution{S}
    untruncated::D      # the original distribution (untruncated)
    lower::Float64      # lower bound
    upper::Float64      # upper bound
    lcdf::T             # cdf of lower bound
    ucdf::T             # cdf of upper bound

    tp::T               # the probability of the truncated part, i.e. ucdf - lcdf
    logtp::T            # log(tp), i.e. log(ucdf - lcdf)
end

### Constructors

function Truncated(d::UnivariateDistribution, l::Float64, u::Float64)
    l < u || error("lower bound should be less than upper bound.")
    lcdf = isinf(l) ? 0.0 : cdf(d, l)
    ucdf = isinf(u) ? 1.0 : cdf(d, u)
    tp = ucdf - lcdf
    Truncated{typeof(d), value_support(typeof(d)), eltype(params(d))}(d, l, u, lcdf, ucdf, tp, log(tp))
end

which I can put in a pull request if it's useful.

[gabrielgellner]

Make a PR!

[cossio]

Why the lower/upper bounds have to be Float64?