Calculating the mean and percentiles of a distribution function

[milo0071]

I have a fairly complicated pdf for Brownian motion with drift for first passage time and would like to calculate the mean and percentiles of the pdf. Is there a straightforward way of going about this? I can plot the distribution.

 

[bpet]

For the percentiles you'll need the cdf.

 

[EnumaElish]

I'll suggest simulation; unless you need to express them as algebraic expressions.