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The variable is a sum of two random variable which obey gamma and uniform distributions, respectively. The parameters of the uniform distribution variable are determined, and the other's must be retrieved from real time calculation.

I want to find the boundary of the summed variable, like using a three sigma rule would do for a normal distribution. Is there any good method to estimate that?

Some inequality, like the Chebyshev inequality, might be too generic of a method so that it will not perform exactly as the three sigma rule would.

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If you would like this question to live here instead of on math.SE, please flag your question over there and either ask that it be deleted or migrated (and merged) here. Cheers. – cardinal May 3 '12 at 12:45
I have flag my post there. – Readon Shaw May 3 '12 at 13:41
Are you asking how to calculate quantiles for the distribution of variables defined as the sum of a uniform and a gamma random variable? – Macro May 5 '12 at 23:54
Yes, the quantile function is exactly what i wanted. I tried to use characterization function of the sum to get CDF and inverse it. but the process is too hard to operate, specially for the complexity of integration. – Readon Shaw May 6 '12 at 2:11

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