I am modelling the parameters that describe the distribution of my observations. For example, let’s pretend I am modelling the \mu and \sigma of my normally distributed observations. Now, I would like to compute the distribution of the percentile of score; that is, I would like to know the distribution of the proportion of values above a threshold. What is the smart way to do that?
One idea comes to mind. For each combination of parameters in the trace \mu and \sigma, I generate (say) 100 samples from the normal distribution, and I compute the percentile of score. Would that be reasonable?