Effect on probabilities and quantiles of adding a quantity with small variance |
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Authors: | R Willink |
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Institution: | Industrial Research Limited |
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Abstract: | This paper gives simple approximations for the distribution function and quantiles of the sum X + Y when X is a continuous variable and Y is an independent variable with variance small compared to that of X . The approximations are based around the distribution function or quantiles of X and require only the first two or three moments of Y to be known. Example evaluations with X having a normal, Student's t or chi-squared distribution suggest that the approximations are good in unbounded tail regions when the ratio of variances is less than 0.2. |
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Keywords: | approximation convolution perturbation quantile sum of random variables |
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