ENH: stats: add array API-support

[mdhaber]

Towards gh-18867

This issue tracks progress toward the addition of array-API support to scipy.stats functions. The functions listed below look ready for conversion, and I'd be happy to review PRs for them. Priority, balancing the ease and importance of the task, is roughly in the order listed.

• moment (ENH: stats.moment: add array API support #20292)
• skew (ENH: stats.skew: add array-API support #20541 - please see this PR as an example roughly similar kurtosis through directional_stats)
• kurtosis (ENH: stats.kurtosis: add array API support #20658)
• describe (ENH: stats.describe: add array API support #20667)
• mode
• entropy (ENH: stats.entropy / special.entr / special.rel_entr: add array API support #20673)
• variation (ENH: stats.variation: add array-API support #20647)
• sem (ENH: stats.sem: add array-API support #20631)
• kstat (ENH: stats: add array-API support to kstat/kstatvar #20634)
• kstatvar (ENH: stats: add array-API support to kstat/kstatvar #20634
• circmean (ENH: stats.circ___: add array-API support #20595)
• circvar (ENH: stats.circ___: add array-API support #20595)
• circstd (ENH: stats.circ___: add array-API support #20595)
• directional_stats
• pearsonr (ENH: stats.pearsonr: add array API support #20284)
• linregress - cov doesn't
• ttest_1samp (ENH: stats.ttest_1samp: add array-API support #20545 - please see this PR as an example for ttest_rel through normaltest)
• ttest_rel
• ttest_ind
• skewtest (ENH: stats.skewtest: add array-API support #20597)
• kurtosistest
• jarque_bera
• normaltest
• power_divergence (for simplicity, split off old version, which supports masked arrays)
• chisquare

After that:

• write a function for computing weighted average. Consider making it public, since it doesn't look like array API will standardize it (Could mean accept an optional weights parameter? data-apis/array-api#366), and it's within our purview. I think it is justifable to just call it mean and make it behave like all the rest of our stats functions - avoiding excess noise, including nan_policy, etc. If that is accepted, might as well add var, too.
• gmean
• hmean
• pmean

After that:

• add N-D support to _array_api.cov; consider making it public if array API won't offer it
• linregress: add axis and array API support
• ks_2samp: consider natively vectorizing, then adding array API support
• bartlett: consider natively vectorizing, then adding array API support
• levene: consider natively vectorizing, then adding array API support
• anserson_ksamp: might be able to vectorize, then add array API support
• wasserstein_distance: consider natively vectorizing, then adding array API support
• energy_distance: consider natively vectorizing, then adding array API support

I'd like to implement the following using _masked_array (gh-20363):

• tmean
• tvar
• tmin
• tmax
• tstd
• tsem

These functions are held up by rankdata (possibly among other things), which is itself in need of improved array-API support. See gh-20639.

• kendalltau
• mannwhitneyu
• wilcoxon
• kruskal
• cramervonmises_2samp
• friedmanchisquare
• brunnermunzel
• ansari
• fligner
• mood

These functions need median, quantile, or similar, either directly or via iqr. See data-apis/array-api#795.

• iqr
• siegelslopes
• theilslopes
• median_test
• median_abs_deviation
• epps_singleton_2samp
• levene (optional)
• fligner (optional)
• sen_seasonal_slopes

I am not interested in supporting the following functions: bayes_mvs, mvsdist, the frequency statistics, weightedtau, somersd or other tabular methods, multiscale_graphcorr.

Many other functions are not listed here because they really need special function support to be useful.

I wrote the following functions, so I'd prefer to do the upgrades on those personally.

• monte_carlo_test (ENH: stats.monte_carlo_test: add array API support #20604)
• permutation_test
• bootstrap
• goodness_of_fit
• power
• false_discovery_control
• differential_entropy