I have a few questions about generalizations of the CLT and stable distributions. I'm trying to correct my understanding and make it precise. Please forgive my naivete, I am not a professional statistician :-)
If I take the sum of a large enough sequence of independent R.V.'s, do they always converge to a stable distribution? (I've heard about generalizations of the CLT, but I'm looking for more precision).
When working with real data, what would be a hint that I need to model with a stable distribution? Is it possible to perform max likelihood with stable distributions?