[Feature Request] Unify `Support` syntax for all Distributions

[Freymaurer]

Is your feature request related to a problem? Please describe.
The syntax for the static member Support ... functions are written in a different syntax.

Bernoulli has a list, whereas hypergeometric returns a tuple.

FSharp.Stats/src/FSharp.Stats/Distributions/Discrete.fs

Lines 55 to 57 in 262f1ac

	static member Support p =
	bernCheckParam p
	[0.0; 1.0]

FSharp.Stats/src/FSharp.Stats/Distributions/Discrete.fs

Lines 228 to 230 in 262f1ac

	static member Support N K n =
	hypergeoCheckParam N K n
	(0., System.Double.PositiveInfinity)

Describe the solution you'd like
Maybe use this issue to discuss not only unifying the syntax, but reworking it to be more intuitive and usable.

[bvenn]

I think the best way to model the support is to use FSharp.Stats.Inverval<'a>. Intervals support generic type inputs, therefore even multidimensional distributions would be covered.

[smoothdeveloper]

FSharp.Stats/src/FSharp.Stats/Intervals.fs

Lines 7 to 9 in 7de8b82

	type Interval<'a> =
	| ClosedInterval of 'a * 'a
	| Empty

We may consider having static member (for overloads) or at least the first one:

ofTuple: ('a * 'a) -> Interval<'a>
ofTuple: ('a * 'a) option -> Interval<'a>

Should the implementation do a comparison in case the values are swapped, and what should occur if they are?

Also, may be useful to offer the reverse:

toTuple: 'a Interval -> ('a * 'a) option

If the type is meant only for closed interval (rather than a larger set of those), maybe it is better to just name it ClosedInterval also.

[bvenn]

Totally agree to the ofTuple and toTuple member:+1:

I'm not sure if in any case it is allowed to have endValue < startValue. I dont't think so and therefore I would add a check that fails if the input is meaningless.

It may be an option to update the Interval type with a Type property that sets if the interval is closed/halfopen_right/halfopen_left/open.

[github-actions]

🤖 This is an automated response from Repo Assist.

This is a good consistency improvement. The current state is:

• Bernoulli — returns a list of supported values ([0; 1])
• Hypergeometric (and several other discrete distributions) — returns a tuple (min, max)
• Continuous distributions generally don't expose Support at all

The direction discussed above (use FSharp.Stats.Interval<'a>) seems right. Interval<'a> already exists in the library and represents a closed [start, end] range, which is the natural representation for a continuous support. For discrete distributions the interval would represent the integer range and callers would know the step is 1.

A concrete migration path:

1. Add ofTuple: ('a * 'a) -> Interval<'a> and toTuple: Interval<'a> -> ('a * 'a) helpers to Interval (discussed here).
2. Change all Support members to return Interval<float> (or Interval<int> for purely-integer discrete distributions).
3. For distributions with a single-point support (edge cases like a degenerate distribution) an Interval still works: Interval(v, v).

For distributions with non-contiguous support (e.g. Bernoulli, which only takes values {0, 1} but not 0.5) the Interval abstraction is a slight over-approximation, but it is still useful for bounding purposes and is consistent with how most statistics libraries handle this.

This is a breaking change for any code currently calling the tuple-returning Support members, so it would need a major version bump or a deprecation cycle. Flagging for maintainer awareness.

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