ENH: stats.skewtest: add array-API support

[j-bowhay]

Reference issue

Towards #20544

What does this implement/fix?

Adds array API support to stats.skewtest

Additional information

[mdhaber]

On my phone this looks really good! I'll take a closer look (including at your where question) when I'm at a computer.

[mdhaber]

Re: CI failure, see https://github.com/scipy/scipy/pull/20595/files#r1582010187

[j-bowhay]

Re: CI failure, see https://github.com/scipy/scipy/pull/20595/files#r1582010187

I am not sure I quite follow, I am not passing in xp to xp_assert_close?

EDIT: ah wait I see 🤦

[lucascolley]

diff LGTM apart from the unresolved comment about nan_policy! I haven't checked thoroughly whether anything else is needed.

[j-bowhay]

Ok CI is green, hopefully that is all comments addressed

[lucascolley]

feel free to merge @mdhaber

[mdhaber]

I think this is fine except for question of default rtol of xp_assert_close. What do you think of it based on what it does for this PR and gh-20595? I think other maintainers need to be aware and on board before we pull the trigger. Are either of you willing to champion this, maybe submitting it as a separate PR? I have another RFC I'll be attending to this week (new distribution infrastructure).

But @j-bowhay please feel free to start on another conversion in the meantime, if you'd like!

[mdhaber]

I didn't think about this carefully before, and I had it like this. But I started wondering whether it should be:

Suggested change

	floating = xp.isdtype(desired.dtype, ('real floating', 'complex floating'))
	if rtol is None and floating:
	rtol = xp.finfo(desired.dtype).eps**0.5 * 4
	floating = xp.isdtype(actual.dtype, ('real floating', 'complex floating'))
	if rtol is None and floating:
	rtol = xp.finfo(actual.dtype).eps**0.5 * 4

If the developer decides to turn off the dtype check, what do they expect to happen when the dtypes are different / what would be most useful?

Suppose rtol is based on the reference dtype (as it is now).

• If we are comparing a low-precision actual value against a high-precision reference, that is too hard of a test to pass.
• If we are comparing a high-precision actual value against a low-precision reference, that is too easy of a test to pass.

So perhaps this should be the other way around - the actual value should be compared against the reference value according to the actual value's own precision.

[mdhaber]

Merged main. If tests still pass, I'll go ahead and merge.