[ENH] Add BurrIII, BurrXII, FDist, FatigueLife, GeneralizedPareto, Levy, Skellam, TruncatedPareto distributions

[arnavk23]

Reference Issues/PRs

Towards #22

What does this implement/fix? Explain your changes.

Does your contribution introduce a new dependency? If yes, which one?

What should a reviewer concentrate their feedback on?

Did you add any tests for the change?

Any other comments?

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For new estimators

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[fkiraly]

Thanks - looks AI generated, and incomplete.

If you use AI, you need to check for mistakes and hallucinations.

• please complete docstrings with an explanation of the distribution, e.g., by giving its definition through pdf or cdf.
• some distributions simply return np.nan through _mean, etc. This overrides the ppf-quadrature based default, so it is not useful.
• there is already a standing scipy adapter which you can use, instead of copy-pasting multiple times the calls to scipy. Please refer to existing distributions that use the scipy backend.

[arnavk23]

• some distributions simply return np.nan through _mean, etc. This overrides the ppf-quadrature based default, so it is not useful.

This pr was not generated by any LLM. Point 1 was a welcome addition (I had done the calculation but forgot to add) Point 2 also another welcome addition but I didn't know about Point 3 (Thank you)

• Docstrings for BurrIII, BurrXII, FDist, FatigueLife, Skellam, and TruncatedPareto have been completed with mathematical definitions and explanations of their distributions. If you need further improvements or want similar updates for other files, let me know!
• The overrides for _mean and _var in TruncatedPareto have been removed. The class will now use the default quadrature-based computation for these methods, as intended.
• All new distributions (BurrIII, BurrXII, FDist, FatigueLife, Skellam) have been refactored to use the ScipyAdapter for consistency and code reuse. TruncatedPareto is a custom case and not a direct scipy distribution, so it was not adapted.

[arnavk23]

@fkiraly
new_distributions_calculations.pdf
Please see the calculations below.

[fkiraly]

This pr was not generated by any LLM.

Ok, I see - it is fine to use AI (I also do), but you need to check what it does.
Empty functions or changes in unrelated files are very typical, the functions that returned np.nan were why I thought this was AI.

It does not make sense to return a dataframe full of nans, if the default already implements a quadrature mean.

[arnavk23]

It does not make sense to return a dataframe full of nans, if the default already implements a quadrature mean.

I agree, that is why I was working on it (which I should've put in a draft pr). Review this pr with a bit of more scrutiny still. Many files are here so mistakes can still be hidden somewhere but I have tried my best.

[fkiraly]

I think this is still not good, and AI generated content / hallucinations remain.

• the _ScipyAdapter is not properly used. Have a look at how, say, Gamma looks like.
• there are still instances of AI problems in the code. If you use AI, please ensure you go through and check.
• the API test contract should not be changed with stepouts for individual distributions. Instead, you can skip an individual test, but please comment on what does not work. Or, if you think the API contract should change, please explain.

[arnavk23]

* the API test contract should not be changed with stepouts for individual distributions. Instead, you can skip an individual test, but please comment on what does not work. Or, if you think the API contract should change, please explain.

The only remaining test failure is for BurrIII(c=2.0) variance, where your code returns np.inf and SciPy returns np.nan, so np.allclose(inf, nan) is False. For c <= 2, SciPy returns np.nan for the variance, but the skpro test contract expects a real non-negative value (not nan). Returning np.nan here matches SciPy's behavior and passes the adapter test, but will fail the contract test.

[arnavk23]

@fkiraly If you like, we could also just take out burriii from this pr if all the other files are ok to you and do the implementation in a followup pr if it keeps on causing problems