# Exact percentile of random variables sum

For a list of empirical random variables $x_1, \ldots, x_n$ where each is given by approx. $7000$ sample values, is there a fast way to calculate a $y$% percentile of $\sum_{i=1}^n x_i$? I have asked this qustion on stackoverflow.com as without employing any math the problem is of exponential complexity (basically unsolvable for $n > 4$), to no avail. No specific information about the distributions of $x_1,\ldots,x_n$ is given. They are neither normal, nor symetric. Nor do they have comparable means and ranges. $n$ is expected to be somewhere in the $2,\ldots, 720$ range, hence Central Limit Theorem can be applied only for a subset of required n values. Any hint is much appreciated. Daniel

-
Are the $n$ random variables independent, or do the $7000$ sets of sample values indicate their relationship? –  Henry Oct 27 '12 at 21:31
Henry, they are independent. –  Dan Bencik Oct 28 '12 at 6:41