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Theory & Methods: Effect on probabilities and quantiles of adding a quantity with small variance
Author(s) -
Willink R.
Publication year - 2002
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00223
Subject(s) - quantile , mathematics , variance (accounting) , statistics , variable (mathematics) , distribution (mathematics) , function (biology) , mathematical analysis , accounting , evolutionary biology , business , biology
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.