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Fitting heavy-tailed mixture models with CVaR constraints

Fitting heavy-tailed mixture models with CVaR constraints AbstractStandard methods of fitting finite mixture models take into account the majority of observations in the center of the distribution. This paper considers the case where the decision maker wants to make sure that the tail of the fitted distribution is at least as heavy as the tail of the empirical distribution. For instance, in nuclear engineering, where probability of exceedance (POE) needs to be estimated, it is important to fit correctly tails of the distributions. The goal of this paper is to supplement the standard methodology and to assure an appropriate heaviness of the fitted tails. We consider a new Conditional Value-at-Risk (CVaR) distance between distributions, that is a convex function with respect to weights of the mixture. We have conducted a case study demonstrating e˚ciency of the approach. Weights of mixture are found by minimizing CVaR distance between the mixture and the empirical distribution. We have suggested convex constraints on weights, assuring that the tail of the mixture is as heavy as the tail of empirical distribution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

Fitting heavy-tailed mixture models with CVaR constraints

Pertaia, Giorgi; Uryasev, Stan
Dependence Modeling , Volume 7 (1): 10 – Jan 1, 2019
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Publisher
de Gruyter
Copyright
© 2019 Giorgi Pertaia et al., published by De Gruyter
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2019-0019
Publisher site
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Abstract

AbstractStandard methods of fitting finite mixture models take into account the majority of observations in the center of the distribution. This paper considers the case where the decision maker wants to make sure that the tail of the fitted distribution is at least as heavy as the tail of the empirical distribution. For instance, in nuclear engineering, where probability of exceedance (POE) needs to be estimated, it is important to fit correctly tails of the distributions. The goal of this paper is to supplement the standard methodology and to assure an appropriate heaviness of the fitted tails. We consider a new Conditional Value-at-Risk (CVaR) distance between distributions, that is a convex function with respect to weights of the mixture. We have conducted a case study demonstrating e˚ciency of the approach. Weights of mixture are found by minimizing CVaR distance between the mixture and the empirical distribution. We have suggested convex constraints on weights, assuring that the tail of the mixture is as heavy as the tail of empirical distribution.

Journal

Dependence Modeling – de Gruyter

Published: Jan 1, 2019

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