[feature request] Generic fallback for non-supported distributions ?

[lrnv]

It would be neat if there was a generic fallback for non-supported distributions. I can come up with a simple solution for continuous distributions:

# fallback for UnivariateContinuousDistribution
import Cubature
pcubature(x * Distributions.pdf(X,x), minimum(X), maximum(X))

but i need to think a bit more for discrete infinite supports.

Edit: There is ageneric fallback in Distributions.jl implemented there: https://github.com/JuliaStats/Distributions.jl/blob/master/src/functionals.jl

So maybe this is just an interface issue, Expectations.jl should not throw when it does not know the distribution but simply use the Distributions.jl one. Thanks @devmotion for the link.

[arnavs]

Currently we have

Expectations.jl/src/iterable.jl

Line 81 in 9b99daf

Continuous iterable expectations (no nodes supplied.) =#

, which falls back to Gauss-Legendre for continuous distributions that lack a specified method.

If we're throwing an error instead of using it, that's definitely a mistake. (Though IMO there should be a warning.) I'll look into it.

(There is also

Expectations.jl/src/iterable.jl

Line 116 in 9b99daf

function _expectation(dist::ContinuousUnivariateDistribution, alg::Type{QuantileRange}; n::Int=50, q0::Real=0.001, qN::Real=0.999, kwargs...)

, which integrates over a uniform quantile grid.)

[lrnv]

I think this is the method I hitted :

Expectations.jl/src/iterable.jl

Lines 96 to 108 in c36874e

	function _expectation(dist::ContinuousUnivariateDistribution, alg::Type{Gaussian}; n=500, kwargs...)
	a = minimum(dist)
	b = maximum(dist)
	(a > -Inf && b < Inf) || throw(ArgumentError("The distribution must be defined on a compact interval. If applicable, bound the distribution by truncating, e.g., expectation(truncated(Pareto(),0.0,1000.0)"))
	rawNodes, rawWeights = gausslegendre(n)
	# Transform nodes to proper interval.
	nodes = map(x -> (0.5(b - a)) * x + (a + b) / 2, rawNodes)
	# Add pdf to weights.
	compoundWeights = [rawWeights[i] * pdf(dist, nodes[i]) for i in 1:n]
	# Add scale factor to weights.
	weights = (b - a) / 2 * compoundWeights
	return IterableExpectation(nodes, weights);
	end

In particular with the Pareto case. While Distributions.jl's expectation method handles these cases (infinite support) without any issue.