Effect on probabilities and quantiles of adding a quantity with small variance
by
Robin Willink
Industrial Research Limited

The density of the sum of two independent variables is a convolution, and the corresponding distribution function is often complicated. This talk presents a method of approximation for the distribution function and quantile of 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 quantile of X and require only the first two or three moments of Y to be known. Examples suggest that the approximations are good in unbounded tail regions when the ratio of variances is less than 0.2, for instance where Y is a perturbation variable.

Date received: August 18, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadt-26.