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JuliaEarth / ExtremeStats.jl

Extreme value statistics in Julia
MIT License
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Implement method of moments #2

Open juliohm opened 6 years ago

juliohm commented 6 years ago

Maximum likelihood fits aren't very robust with GEV distributions. It would be nice to implement the method of moments as an alternative.

davidanthoff commented 4 years ago

Are there similar problems with the GP distribution, or is that part more robust?

juliohm commented 4 years ago

Hi @davidanthoff,

I'd have to investigate the theory more carefully to answer it properly. Are you having issues with the GP estimation as well?

davidanthoff commented 4 years ago

No, I'm just starting to play with this, and was wondering whether there was a known problem or not :)

Also, there is https://github.com/jojal5/Extremes.jl, which seems to have MM and some bayesian estimator already? Are there any efforts to merge the two packages? They really seem to do the same thing, right?

juliohm commented 4 years ago

Thank you for sharing the package. Will ask if the author is interested in joining efforts here.

davidanthoff commented 4 years ago

I did try the fit for the GP in both packages, got exactly the same results, so I guess that is a good sign :)

juliohm commented 4 years ago

That is promising at least :)

I hope to get back to extreme value theory at some point. Currently, my research is too focused on GeoStats.jl, and that is demanding a great amount of :hourglass:

Datseris commented 1 year ago

In this library, I have implemented method of moments and probability weighted moments as ways to fit a GPD to data produced using the Peak over Threshold approach:

https://github.com/JuliaDynamics/FractalDimensions.jl/blob/main/src/extremes_based/gpd.jl#L33-L47

The implementations come from the paper: Chaos 33, 073143 (2023) https://doi.org/10.1063/5.0152370

You are interested in section V.A. of the paper, starting at page 6. It shows efficacy of estimators from data sampled directly from a GPD. It shows that maximum likelyhood methods are surprisingly not very good. However the method you have here probably has nothing to do with the method the authors use as "maximum likelyhood".

Datseris commented 1 year ago

(p.s. i'll probably add a method using your package in our FractalDimensions.jl package)

juliohm commented 1 year ago

It would be awesome to add the method of moments here as well @Datseris so that it reaches a broader audience ❤️