# Interpretation of a Gumbel distribution's results

I am using (essentially) the approach outlined in the paper "Statistical-based WCET estimation and validation" (http://drops.dagstuhl.de/opus/volltexte/2009/2291/pdf/Hansen.2291.pdf) to build a Gumbel distribution for worst-case execution times for a real-time software system.

To model the distribution I build a data set out of, say, the worst time in 32 successive executions of the benchmark I am using. I might then get 40 or 50 such data points and using some R get a figure for $$\mu$$ and for $$\beta$$ and from there can, say, get a figure for the limit for $$10^{-5}$$ or $$10^{-6}$$ cases.

The question is, though, is this (in some say) a measure of the worst $$\frac{1}{100000}$$ or $$\frac{1}{1000000}$$ of what are already the worst cases or a statement about the expected value of one-in-a-million (or so on) of all cases?

You are estimating a lower bound on how bad the worst $$10^{-6}$$ of data points would be. "Data points" being what you fed in: in your case, the worst of 40-50 execution times.