Clarify and enhance descriptive statistics (and more)

[kcrisman]

We have some basic statistics functionality in ​sage stats for some descriptive statistics. Unfortunately, it is really basic.

This ticket is for clarifying the relationship of that material to the Sage ​probability distributions, histogram, Scipy, GSL, and other libraries - perhaps including pandas, though this is not (yet) standard in Sage.

• Ideally there would be interfaces to the best native Python functionality rather than something specific to Sage (though that may not be possible).
• There may be a tutorial page in the (reference manual) documentation for demonstrating best practices.
• There could be a more education-oriented tutorial elsewhere, along the lines of ​the PREP Quickstart but more comprehensive.
• As noted at #29662, Python 3 has a ​stats module, though presumably that module can't handle (say) the mean of several Integers or even stranger objects, as-is.

If all of those generate interest, this ticket would be converted to a metaticket to keep track of them.

[dunfield]

I use pandas pretty heavily from within Sage (Python 2.7 version). The only problem I encounter has to do with pandas not recognizing Sage's Integer as an integer. Assuming one has the standard preparser on, you have to do things like:

dataframe.loc[int(100)]
dataframe.apply(some_function, axis=int(1))

to keep it happy.

[kcrisman]

I use pandas pretty heavily from within Sage (Python 2.7 version).

Hmm, yeah that is exactly the kind of problem I expected (brian had some similar issues iirc). I assume you pip install it, not included in our Python from the get-go, right?

[dunfield]

Replying to kcrisman:

I assume you pip install it, not included in our Python from the get-go, right?

Yes, I just use pip install which has always worked smoothly (though it takes a bit of time to compile). The main dependency is just a reasonably recent version of numpy which of course Sage has.

[gh-sheerluck]

Replying to dunfield:

pandas not recognizing Sage's Integer as an integer.

I added

from sage.rings.integer import Integer
if type(key) is Integer:
    ...

to pandas/core/indexes/{base,range}.py