NIG, stretched exponential and Levy stable estimation

#1
Hello to all,
I'm currently studying the distribution of returns of stock market indexes, and I would like to do some hypothesis testing on their distribution. Apart from the gaussian distribution (which poses no problem) I would like to do some tests for Normal inverse gaussian, stretched exponential (double, I guess) and Levy stable distributions. So, my questions are.
-Which are the estimates used for the parameters of these distributions?
-Is the sampling distribution of those guys known or do I have to bootstrap or Montecarlo for hypothesis testing?
Any idea, reference or code is welcome.
Thanks a lot in advance.
All the best.
Pablo