Discrete distributions CDF does not support Inf input

[sparktseung]

I am using Poisson and NegativeBinomial distributions, and it seems that their cdf and logcdf do not support Inf as x input, while pdf and logpdf seem to work fine. The following is an example. It seems natural to require cdf and logcdf to return 1.0 and 0.0, respectively.

julia> pdf(Poisson(5.0), Inf)

0.0

julia> cdf(Poisson(5.0), Inf)
ERROR: InexactError: trunc(Int64, Inf)
Stacktrace:
 [1] trunc at .\float.jl:702 [inlined]
 [2] floor at .\float.jl:363 [inlined]
 [3] cdf(::Poisson{Float64}, ::Float64) at ...\.julia\packages\Distributions\kPXE9\src\univariates.jl:378
 [4] top-level scope at none:0

[sparktseung]

I actually suggest a check on all distributions included in the package. Just tried InverseGaussian, and the same issue occurs.

[mschauer]

A discrete distribution might conceivable have a point mass at Inf so a bit care is needed with the pdf's, the cdf will by 1 either way.

[devmotion]

This was fixed, probably by #1348:

julia> cdf(Poisson(5.0), Inf)
1.0