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

Abstract

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

Castellacci, Giuseppe, A Formula for the Quantiles of Mixtures of Distributions with Disjoint Supports (May 9, 2012). Available at SSRN: https://ssrn.com/abstract=2055022 or http://dx.doi.org/10.2139/ssrn.2055022

Giuseppe Castellacci (Contact Author)

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
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New York, NY 10003-711
United States

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