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 :)

Chances are that the best answer is in some book titled "Non-parametric statistics." I don't know the texts in the field so I can't suggest one.
On the other hand, it's probably not that hard to get close to what you want using a heuristic method, guided perhaps by some experimentation. 
If the sample was very large, you could take the 90 percentile point. I would adapt this idea to small sample sizes with the added rule that the prediction would be equal to one of the values in the set. 
For set S with N observations sorted in ascending order indexed by i, the rule would be something like this:
For N <=9, prediction = x[9]
For N > 9 and N < 20, prediction = x[N-1]
For N > 20 and N < 40, prediction = x[N-2]
Note that I'm only suggesting the form of the answer, not the actual rule, and in fact, I'm really only suggesting that you base your prediction on the upper tail of the sample.
