I want to get a confidence interval of a function of some parameters. for example, from the data I estimate parameters of Pareto. Now I want to get 95% CI for 90th quantile (it's a function of parameters of Pareto), so I would need standard error.
I know delta method is one option. For simulation method, I am wondering if it is legitimate to simulate 1000 samples of size 50 from Pareto, calculate each of the 90th quantiles and take the standard deviation of the 1000 data. Is the standard deviation I get equivalent to standard error? Thanks for your help!