What method (ML, quantile, etc) does MATLAB use when fitting stable distributions to data?

I can't determine find a reference to which method/algorithm MATLAB uses to fit a stable distribution to my data. There are several methods in the literature, including maximum likelihood, quantile, fractional lower order moments, etc. Some of these methods have limited accuracy when the data falls into extreme values of the stable parameters, particularly \alpha.

I've checked the following pages:

https://www.mathworks.com/help/stats/stable-distribution.html

https://www.mathworks.com/help/stats/prob.stabledistribution-class.html

I might have not found the correct page or document...does anyone know the answer or right reference?

[Astarag Chattopadhyay]

Hi,

I would suggest you to go through the reference papers provided at the bottom of the page in the following link provided by you:

https://www.mathworks.com/help/stats/stable-distribution.html

It may give you some perspective about the algorithm MATLAB uses to fit a stable distribution to data.