ENH: use analytical formula in scipy.stats.powerlaw._munp().

[fancidev]

Reference issue

Closes gh-20036.

What does this implement/fix?

Use analytical formula in scipy.stats.powerlaw._munp. The formula is derived by simple integration, and elaborated in gh-20036.

Additional information

A simple unit test case is supplied.

[fancidev]

Are there difficulties for very high moments for the powerlaw distribution?

No, the expect function works perfectly fine for 5th moment and only starts to lose precision when moment > 10000.

I did a quick search for a common moment test but didn’t find one, so I wrote the custom test. Thanks for pointing it out!

I’ll make an update commit to remove the custom test.

[mdhaber]

@dschmitz89 I'll let you use the new big green button on this one! (Sounds like it will appear in your interface soon if it hasn't already.)

[fancidev]

@dschmitz89 Could you please merge and close this PR?

[dschmitz89]

@fancidev I do not have commit rights, so cannot merge. You could not know that though, that's fine :). Still, I would rather not discuss scipy's ACL openly here.

[fancidev]

@fancidev I do not have commit rights, so cannot merge. You could not know that though, that's fine :). Still, I would rather not discuss scipy's ACL openly here.

Understood. I implied that when @mdhaber mentioned about the “new big green button” :-)

[dschmitz89]

Thanks @fancidev !