Statistics: Predict 90th percentile with small sample set I have a quite small data set (on the order of 8-20) from an essentially unknown system and would like to predict a value that will be higher than the next number generated by the same system 90% of the time. Both underestimation and overestimation are problematic.
What is the mathematically "correct" way to do this?
If I could also generate a level-of-confidence estimate, it would wow my manager.
Also, let me say I'm not a math major, so thanks for any help, however remedial it may be :)

This is where the technique of "Bootstrap" comes in extremely handy. You do not need to know anything about the underlying distribution.
Your question fits in perfectly for a good example of "Bootstrap" technique. The bootstrap technique would also let you determine the confidence intervals. Bootstrap is very elementary to implement on computer and can be done really quick. The typical number of bootstrap samples you take is around $100-200$.
Go through the wiki page and let me know if you need more information on "Bootstrap" technique and I am willing to help you out.
The book by Bradley Efron covers this technique from an application point of view in great detail. The bootstrap algorithm for estimating standard errors is explained on Page $47$, Algorithm $6.1$. You can use this algorithm to construct confidence intervals and finding the quantiles.
