rand( TDist(Inf) ) gives NaN in v0.20.0

[atteson]

I noticed that rand( TDist(Inf) ) gives NaN in v0.20.0 but gives a value in v0.16.4 (which I assume corresponds to a standard normal variate).

pdf( TDist(Inf), 1.0 ) works fine in both versions.

[matbesancon]

Several issues here, the distribution parameter should not be taking a real type but an integer value. The type parameter could capture in some sense the infinite / finite thing and dispatch accordingly.

The documentation is also pointing to the "student" wikipedia page, which is not the Student distribution page.
PR welcome

[atteson]

Actually, the t distribution is perfectly well defined for integer values of nu and I (and others) use it that way.

[johnczito]

I think the change happened here, where

rand(d::TDist) = StatsFuns.RFunctions.tdistrand(d.ν)

became

rand(rng::AbstractRNG, d::TDist) = randn(rng) / sqrt(rand(rng, Chisq(d.ν))/d.ν)

The denominator becomes sqrt(Inf/Inf) = NaN. So do we want something like this?

rand(rng::AbstractRNG, d::TDist) = randn(rng) / ( isinf(d.ν) ? 1 : sqrt(rand(rng, Chisq(d.ν))/d.ν) )

[atteson]

My preference is to allow for the nu=Inf to mean the normal distribution since this is always the limiting behavior. I like the way the R function works. However, there are other limiting cases which are not handled in Distributions. For example, a normal with sigma=0 doesn't become a delta distribution.

[johnczito]

Right, so you want TDist(Inf) to simply return Normal(0,1). That makes sense, though I'm not sure what the type stability implications of that are.

[atteson]

Actually, my intent is that TDist( Inf ) remain that type but act like Normal(0,1) in rand, pdf, cdf, etc. I think that's probably better because of type stability as you mention. Someone might assign these to a Vector{TDist} or some such.

The bigger question is "what's the policy of Distributions for edge cases"? Some approaches that I see are:

1. Make the distribution behave as the limiting distribution in the edge cases (at least when there is a limiting distribution under no other conditions).

2. Have the distribution fail in the edge cases.

3. Have the functions of the distribution return NaN.

#1 is what TDist(Inf) used to do. #2 is what Normal(0,0) does. #3 is what TDist now does.

My preference is for #1 though this becomes subtle for multivariate distributions. A multivariate normal with a singular covariance matrix is a normal on a lower dimensional linear subspace.

[johnczito]

That all sounds right to me. You said pdf is behaving. So for rand we could do something like this and it should work again:

rand(rng::AbstractRNG, d::TDist) = randn(rng) / ( isinf(d.ν) ? 1 : sqrt(rand(rng, Chisq(d.ν))/d.ν) )

[atteson]

Sounds good.