DOC: clarify parameters of norminvgauss in scipy.stats

[chrisb83]

Reference issue

Closes gh-14568

What does this implement/fix?

Explain alternative parametrization of norminvgauss

Additional information

I updated the tutorial and documentation of norminvgauss

[josef-pkt]

LGTM

That's helpful
I didn't check the math.

[mdhaber]

The math looks right. We could spend a lot of time trying to get the appearance of code and math right and make the correspondence (e.g. between α and alpha) explicit, but it's really hard to satisfy everyone, so I'll ignore it.

@Nishan-Pradhan can you confirm that this resolves the issue? You mentioned that you did some tests; can you paste some of that here - an example of TF code, equivalent SciPy code according to the note in this PR, and results that show they're equivalent? If so, I'll go ahead and merge.

Thank you!

[Nishan-Pradhan]

Hi @mdhaber, I was unable to compare the SciPy implementation to TF as it seems the TF NormalInverseGaussian is not yet implemented fully, as confirmed here: tensorflow/probability#1398

I have however managed to match up the results of SciPy transformation to an Excel based implementation of the NIG distribution using the mu and delta parameters which leads me to believe that the transformation is correct.

[mdhaber]

Thanks @chrisb83 @josef-pkt @Nishan-Pradhan!