I don't think commercial tools give you the critical path delay distribution; the current approach is to check what happens to critical path in corners (e.g. fat, slow, typical). This can give you an idea of the distribution.

1.to use Hilbert-Huang method  decomposiing the wave;

2. to detecting  the wave phase;

3. to computing the delay.

There is no delay distribution in STA reports, indeed. However, you can enable the ocv mode in PrimeTime and set OCV parameters and timing derating factors. You can enter the pt_shell and do a "apropos ocv" to check which commands are available. 

I am not aware of formal methods, but it seems to me that if you have the distribution for each task on the CP, you could do a Monte Carlo simulation. Basically, do thousands of trials, and for each trial randomly draw a time from each task distribution.

Fast/slow/typical will overestimate the variation, since some variation (e.g. random dopant fluctuation) is uncorrelated. Monte Carlo is the most accurate in commercial tools and OCV your most practical option.