Fix the numerical instability in Truncated.

[MrVPlusOne]

The current constructor for Truncated is not numerically stable, for example,

original = Normal(-5.0, 0.2)
trunc = truncated(original, 0.0, 5.0)
test_point = 0.5
logpdf(trunc, test_point)  # returns Inf!

This is because the constructor directly performs the computation using probabilities instead of log probabilities:

function truncated(d::UnivariateDistribution, l::T, u::T) where {T <: Real}
    l < u || error("lower bound should be less than upper bound.")
    T2 = promote_type(T, eltype(d))
    lcdf = isinf(l) ? zero(T2) : T2(cdf(d, l))
    ucdf = isinf(u) ? one(T2) : T2(cdf(d, u))
    tp = ucdf - lcdf
    Truncated(d, promote(l, u, lcdf, ucdf, tp, log(tp))...)
end

This pull request fixes this issue by using logcdf and the numerically stable operation logsubexp.

[codecov-commenter]

Codecov Report

Merging #1374 (2d3e216) into master (e49b844) will increase coverage by 7.24%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #1374      +/-   ##
==========================================
+ Coverage   75.56%   82.81%   +7.24%     
==========================================
  Files         116      116              
  Lines        4903     6661    +1758     
==========================================
+ Hits         3705     5516    +1811     
+ Misses       1198     1145      -53     

Impacted Files	Coverage Δ
src/truncate.jl	85.91% <100.00%> (+7.34%)	⬆️
src/genericfit.jl	66.66% <0.00%> (-8.34%)	⬇️
src/univariate/continuous/studentizedrange.jl	72.72% <0.00%> (-5.06%)	⬇️
src/univariate/continuous/noncentralf.jl	85.00% <0.00%> (-1.67%)	⬇️
src/univariate/continuous/cosine.jl	92.85% <0.00%> (-1.27%)	⬇️
src/univariate/continuous/arcsine.jl	88.57% <0.00%> (-1.09%)	⬇️
src/univariate/continuous/skewnormal.jl	65.62% <0.00%> (-1.05%)	⬇️
src/univariate/continuous/normalinversegaussian.jl	88.46% <0.00%> (-1.02%)	⬇️
src/univariate/discrete/negativebinomial.jl	91.11% <0.00%> (-0.79%)	⬇️
src/show.jl	95.00% <0.00%> (-0.66%)	⬇️
... and 102 more

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[devmotion]

Thank you for the PR and sorry for the delay 🙂