DOC: clarify expect() return val when moment is inf/nan

[rlucas7]

Closes #9259

[rlucas7]

Also, I noticed I had put numeric integration in the discrete method definition. While not incorrect in the Lebesgue measure sense (just switching to counting measure) this is likely unclear to the typical doc reader so in the latest commit (force pushed to remote branch) I changed to numeric summation

[josef-pkt]

To help in understanding the effect of bounds an example in the docstring with integrating constant function might be useful.

i.e. expect of lambda x: 1 is just cdf(ub) - cdf(lb)
if conditional=True, then expect of lambda x: 1 is just 1

[rlucas7]

@chrisb83 , @josef-pkt, I'm new here should I close the PR if all the comments are addressed?

[chrisb83]

Hi, the text is fine, i added a few formatting details. Please don't close the PR, it will be merged by one of the members once approved.

[rlucas7]

@chrisb83, Thanks for all your time (and keen eyes!) so far, super helpful. All check are passing. Do you see any other issues in the commit?

[chrisb83]

Thanks, this looks good now. Only one minor thing: It would be nice to have the examples in a section "Examples" but this can also be done in a later PR.

[rlucas7]

@chrisb83, Thanks! I added in 2 lines separation with "Examples" header in lines 2394 + 2395. Unclear if we want the "for example" examples from the previous ¶ in the new examples section. The doc seems to read better with them in the previous ¶ so I left them in that ¶.

[chrisb83]

I think it is fine, normally the examples are written in a way that the code is run and the user sees the results, see e.g. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.jarque_bera.html
this can also be changed in a follow up PR, in any case, there is more Information for the user now than before.

let's wait a few more days if there is further feedback, otherwise I will merge it

[rlucas7]

let's wait a few more days if there is further feedback, otherwise I will merge it

will do.

[rlucas7]

@chrisb83, it's been a few days and no one has responded. Should I ping the others contributors on the PR?

[ilayn]

Sorry for the last minute review but can we make this as code examples

To understand the effect of the bounds of integration consider

    >>> from scipy.stats import expon
    >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0)
    0.6321205588285578

This is close to 

    >>> expon(1).cdf(2.0) - expon(1).cdf(0.0)
    0.6321205588285577

If ``conditional=True``

    >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0, conditional=True)
    1.0000000000000002

The slight deviation from 1. is due to numerical integration.

[rlucas7]

@ilayn, thanks. I added the examples docstring similar to how you have it here. and pushed. The builds all seem to pass except the Travis build which only fails on python 3.5 and the tests that are failing are totally unrelated (in signals sub-module)-or at least appear to be-to the changes. All other python versions in the travis build pass the checks. Maybe these are some flaky tests?

[ilayn]

The fails are unrelated (I'll submit a PR).

So thanks @rlucas7 @chrisb83 merging.

[rlucas7]

@ilayn + @chrisb83 Thanks for shepherding me through this process! 👍