ENH: moments for the zipf distribution

[ev-br]

Should close gh-1886.
A remaining issue is that expect reports the lack of convergence for small enough values of a. Which is a known issue (and the knownfail I'm leaving in this PR can serve as a useful smoke test if/when discrete expect is improved).

[josef-pkt]

Can you copy the code for the failing expect kurtosis test in an issue? It's faster to replicate than looking at the changeset or test code.

zipf.expect(...
zipf.stats(...

It's possible that the expect in expect stops to early in the tail in this case, (x - mean)**4 can get pretty large.
(but I still find it a bit surprising)

[josef-pkt]

expect is hitting maxcount which seems to be too low in this case, and it's not an option currently

[ev-br]

Here it is:

>>> m, v, s, k = stats.zipf.stats(6.5, moments='mvsk')
(array(1.0130420979439105), array(0.015940729460401704), array(12.561822558088409), array(279.4461024600989))
>>> stats.zipf.expect(lambda x: np.power(x-m, 5), args=(6.5,))
/home/br/virtualenvs/scipy-dev/local/lib/python2.7/site-packages/scipy/stats/distributions.py:7065: RuntimeWarning: expect(): sum did not converge
  warnings.warn('expect(): sum did not converge', RuntimeWarning)
0.666271192853372
>>> (k+3)*v*v
0.071771491009249733

Sure, the power is low, the sum does not converge all that well.

[josef-pkt]

you did power 5 not 4

using still scipy 0.9

>>> m, v = stats.zipf.stats(6.5)
>>> m, v
(array(1.0130420979439105), array(0.015940729460401704))
>>> m3 = stats.zipf.expect(func= lambda x: (x-m)**4, args=(6.5,))
sum did not converge
>>> m3
0.071753510989155736
>>> ke = m3 / v**2 - 3
>>> ke
279.37534474660725
>>> ke / 279.4461024600989 - 1   # relative error
-0.00025320701512299149

[ev-br]

Argh.what was it about learning to copy-paste if I can't do the numbers. It's 4 in the test (common_tests.py)

[josef-pkt]

Ok expect bug, needs better or optional termination condition. `maxcount`` is mainly a safeguard and I picked the number under the assumption that it won't be triggered under regular circumstances.

[rgommers]

Rebased and fixed a couple of minor PEP8/style issues at https://github.com/rgommers/scipy/compare/pr;2904. This fixes a test failure I've been seeing for weeks, so can we merge this?

[ev-br]

IMO, it's ready to go in. The issue with the 4th order moment is an expect problem: the convergence rate of the sum is slow. Maybe needs a Levine u-transform --- but that's a separate story.

[ev-br]

Also, it seems to me that gh-1329 can now be closed --- I'm not claiming there are no problems left :-), but at least all problems smoked out in there are either fixed or marked as a known failure (of which there's only a handful left.)

[josef-pkt]

looks fine to me

[rgommers]

OK merged in 9dd997c. Thanks Evgeni, Josef.