BUG: Avoid cancellations in nanskew/nankurt.

[jvkersch]

closes #11974

This replaces the implementation of nanskew and nankurt by an algorithm that does not produce round-off error due to subtracting very similar large values. The sample skew and kurtosis are computed directly from the moments, rather than expanding the moments, which leads to cancellation errors. The algorithm implemented here is about as efficient as the original implementation (in terms of time and memory); a more efficient one-pass algorithm is certainly possible but would require some Cython code.

[jreback]

add the issue number here as a comment

[jreback]

very minor change. pls rebase. ping when ready.

[jreback]

maybe add parens for clarity of precedence?

[kawochen]

In computing skewness, is the computation of m3 still potentially unstable? (Just wanted to understand the new behavior)

[jvkersch]

@jreback Thanks for the quick review. I made the changes, and Travis passes.

@kawochen Not sure why you refer to m3 explicitly, but while the calculation with the moments can also be unstable (e.g. when you have a series with huge values and a huge mean), it should be much less so than the previous implementation, which does things like (x ** k).sum() - x.sum() ** k, which quickly picks up a lot of round-off error.

[kawochen]

@jvkersch I referred to m3 because that was one of the calculations that could benefit from doing the positive and negative parts separately. Symmetric samples would have a 0 skew more often. But the final skew numbers of symmetric samples are close enough to 0 as they are, so I'm just pointing that out, but not suggetsing that we do that.

[jreback]

@jvkersch thanks!

[jvkersch]

@kawochen I see, that makes sense; I didn't think about the alternate signs. Thanks for the clarification.