ENH: Implement Kendall discordance

[fbourgey]

Reference issue

Toward #98

What does this implement/fix?

Implement Kendall discordance from _kendall_dis

[mdhaber]

This looks like a faithful translation, and the tests are OK with my if they're ok with @steppi.

The tests are a little light, so I would suggest a few larger, non-trivial examples (probably randomly generated), and also checking behavior when there are tied elements. Maybe run kendalltau with randomly generated x and y (with and without the possibilities of ties in x, ties in y, and both) up until you get to dis = _kendall_dis(x, y) # discordant pairs to see what sort of input _kendall_dis can receive.

Thank you!

@steppi if we use this in SciPy, can it automatically be vectorized to work along the last axis?

[fbourgey]

This looks like a faithful translation, and the tests are OK with my if they're ok with @steppi.

The tests are a little light, so I would suggest a few larger, non-trivial examples (probably randomly generated), and also checking behavior when there are tied elements. Maybe run kendalltau with randomly generated x and y (with and without the possibilities of ties in x, ties in y, and both) up until you get to dis = _kendall_dis(x, y) # discordant pairs to see what sort of input _kendall_dis can receive.

Thank you!

@steppi if we use this in SciPy, can it automatically be vectorized to work along the last axis?

Thanks @mdhaber, I'll improve the tests.

[fbourgey]

@mdhaber I have improved the tests with randomly-generated and tie/no-tie scenarios for x and y.

Can you detail exactly what you meant with

[...] up until you get to dis = _kendall_dis(x, y) # discordant pairs to see what sort of input _kendall_dis can receive.

[mdhaber]

Can you detail exactly what you meant with...

It's probably not very important. I just couldn't remember exactly what could happen with the input to _kendall_dis - I think both x and y are ranks, but I couldn't remember whether there could be tied ranks within x, tied ranks within y, and tied ranks between the two. A little bit of thinking / reading code could help remind me, but the option I was suggesting was generating random input (with ties) to scipy.stats.kendalltau and seeing what data gets passed to _kendall_dis.

[fbourgey]

Can you detail exactly what you meant with...

It's probably not very important. I just couldn't remember exactly what could happen with the input to _kendall_dis - I think both x and y are ranks, but I couldn't remember whether there could be tied ranks within x, tied ranks within y, and tied ranks between the two. A little bit of thinking / reading code could help remind me, but the option I was suggesting was generating random input (with ties) to scipy.stats.kendalltau and seeing what data gets passed to _kendall_dis.

@mdhaber OK, thanks. Do you think the current test is sufficient? Happy to expand on it if needed.