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gmgeorg / LambertW

LambertW R package: Lambert W x F distributions and Gaussianization for skewed & heavy-tailed data
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theoretical kurtosis #2

Closed stephenhky closed 2 years ago

stephenhky commented 2 years ago

In functions such as IGMM and delta_GMM, there is a default input parameter called theoretical.kurtosis, which is usually set to 3. Is there a particular reason why? If I have to provide a theoretical kurtosis, what is the best way to determine the theoretical kurtosis value (not the empirical one)?

stephenhky commented 2 years ago

Never. I got it.

gmgeorg commented 2 years ago

Following up for future reference:

The theoretical.kurtosis gets chosen by the user as a way to characterize the input distribution properties they want to obtain when using the method of moments estimators. It defaults to 3 since thats the theoretical (population) kurotis of a Normal distribution, which is the default for the h and hh type Lambert W x F distributions (in location / scale case). In case you are working with scale family distribution and the observed data looks like a heavy tailed version of an exponential distribution then it may make sense to use theoretical.kurtosis = 9 to obtain a methods of moments estimate for a Lambert W x exponential distribution (since kurotis of an exponential is 9 -- see wiki).