Closed stephenhky closed 2 years ago
Never. I got it.
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).
In functions such as
IGMM
anddelta_GMM
, there is a default input parameter calledtheoretical.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)?