A Formula for the Quantiles of Mixtures of Distributions with Disjoint Supports
11 Pages Posted: 10 May 2012 Last revised: 14 May 2012
Date Written: May 9, 2012
In this note we derive closed formulas for the quantiles of a class of cumulative distribution functions (CDF) that can be expressed as mixtures. Generally quantiles of mixtures are only computable numerically. In this case, we assume that the support of the component densities are disjoint, which allows explicit computation in terms of the quantiles of the component distributions. Such quantiles may be of interest in risk modeling, e.g., piecing together risk profiles (e.g., power law on the left, Student t on the right) that are different for gains and losses in a risk measure.
Keywords: quantile, mixture of distributions, risk measures
JEL Classification: C19, C15, G13
Suggested Citation: Suggested Citation