Quantile of a Mixture
Abstract
In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial information is available (Bernard and Vanduffel (2014)).
- Publication:
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arXiv e-prints
- Pub Date:
- November 2014
- DOI:
- 10.48550/arXiv.1411.4824
- arXiv:
- arXiv:1411.4824
- Bibcode:
- 2014arXiv1411.4824B
- Keywords:
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- Statistics - Other Statistics