Effect on probabilities and quantiles of adding a quantity with small variance
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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