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Method of computing quantiles/distributions of the sum of r....

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Method of computing quantiles/distributions of the sum of r....

Suppose we know the distributions of X1, X2, ..., Xn, any suggesions on how to compute the quantiles/distributions of X1+X2+...+Xn? Note that X1, X2, ..., and Xn may be independent or dependent; they may or may not assume the same pdfs (or pdfs of the same form, e.g., Gaussian).

It has been shown that this computation is NP-hard in general, so I wonder if there is any effective pseudo-polynomial algorithm or approximate algorithms for solving the problem? Any advice will be greatly appreciated.


If they are independent, there is a straightforward procedure. Calculate the characteristic function for each of the variables, multiply them all together and then get the distribution function for the resultant characteristic function (the product). Once you have some dependency it becomes much harder.

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