ENH: Support reduction methods on Index(?)

[mroeschke]

Feature Type

• Adding new functionality to pandas

• Changing existing functionality in pandas

• Removing existing functionality in pandas

Problem Description

In theory, a numeric Index could support reduction functions as a "1D list-like object" and closer align to Series in this way as well. Of course reduction functions might not make sense on some Index subclasses (MultiIndex, IntervalIndex, etc)

cuDF Index supports reduction functions and are considering deprecating them to align with the pandas Index API, but opening this issue to gauge whether pandas actually wants to support reduction functions on Index rapidsai/cudf#12284

Current reduction functions supported on Series:

pandas/pandas/conftest.py

Lines 1036 to 1048 in 36dcf51

	_all_numeric_reductions = [
	"count",
	"sum",
	"max",
	"min",
	"mean",
	"prod",
	"std",
	"var",
	"median",
	"kurt",
	"skew",
	"sem",

Feature Description

Defining _reduce on Index which can dispatch to EA._reduce if an EA type or use a nanop method otherwise?

Alternative Solutions

index.to_series().<reduction_op>(...)

Additional Context

No response

[phofl]

I am not sure what I would use it for. Do you have any examples in mind where this would be helpful?

[mroeschke]

Especially with to_series, I would also say the practical use case isn't that strong. There might be a subset of users who treat Index as an array-like object and might find it convenient to have reductions?

Additionally, Index objects already do support arithmetic and logical operations so there's some notion of Index supporting numeric array like operations.

[phofl]

Ok treating them as an array-like object makes sense. Just asking, because I never had a situation where this would have been helpful.

[jreback]

no objection as long as these dispatch

[jbrockmendel]

+1 on making Index behave like Series where feasible

[jbrockmendel]

xref #54566 moves closer to the pattern suggested here