DOC: added exp weighting clarifications from #8861

[matthewgilbert]

I integrated the comments in #8861 from @seth-p into the exponential weighted moment functions docs.

[jorisvandenbossche]

Thanks! Looks good from a technical point.
@seth-p Can you do a review?

[seth-p]

It looks good, though would be even better to include some of the substance in @immerrr's #8861 (comment), specifically that for the adjust=False case to make sense, you need to assume that "the first element is not an ordinary value, but rather a prior knowledge of the whole infinite-ish series".

[matthewgilbert]

Good point, I'll put some of that content in.

[jreback]

@matthewgilbert pls review the doc string pd.ewma as well for consistency with this (you can also put in a link to the actual docs to not make it overly long)

[matthewgilbert]

@jreback Bit confused with your suggestion to link to the docs string, was there a specific place you had in mind for this?

[jreback]

put a link in the doc-string to the more detailed explanations

[matthewgilbert]

Incorporated link to the docstring and added some explanation of describing assumptions on first element when adjust=False, squashed this into one commit

[seth-p]

@matthewgilbert, I'm afraid I don't think you incorporated @immerrr's point in #8861 (comment) correctly. It is when adjust=False that one is implicitly assuming that x[0] is a moving average encapsulating the data from all "previous" observation; whereas for adjust=True one is implicitly assuming that x[0] is an observation just like every other x[i], i>0. (In all of these, 0 should really be replaced by the index of the first non-NaN value in x[], but I'm glossing over that subtlety.)

[matthewgilbert]

@seth-p Thanks, yes this was a typo, sorry about that. Just to be clear, changing

"When adjust=True we have..." to "When adjust=False we have..." should fix this, or is there something else I'm missing?

[seth-p]

@matthewgilbert, I think that's fine, though also I think :math:\alpha x_t + (1 - \alpha) y_{t-1} should be `:math:`y_t = \alpha x_t + (1 - \alpha) y_{t-1}.

[matthewgilbert]

All comments have been incorporated. I squashed this all into one commit so unsure if as a result this does not send notifications and thought I would just comment here to be sure.

[jreback]

@matthewgilbert yes a push does not ping anyone.

This looks good.

@seth-p any final comments?

[seth-p]

Looks good.

[jorisvandenbossche]

@matthewgilbert Thanks a lot!
In some time, this should be built in the dev docs: http://pandas-docs.github.io/pandas-docs-travis/, so you can always check there if everything looks fine