The Lila distribution and its applications in risk modelling

Abstract : Risk date sets tend to have heavy-tailed, sometimes bi-modal, empirical distributions, especially in operational risk, market risk and customers behaviour data sets. To capture these observed “unusual” features, we construct a new probability distribution and call it the lowered-inside-leveraged-aside (Lila) distribution as it transfers the embedded weight of data from the body to the tail. This newly constructed distribution can be viewed as a parametric distribution with two peaks. It is constructed through the composition of a Sigmoid-shaped continuous increasing differentiable function with cumulative distribution functions of random variables. Examples and some basic properties of the Lila distribution are illustrated. As an application, we fit a Lila distribution to a set of generated data by using the quantile distance minimisation method (alternative methodologies have been tested too, such as maximum likelihood estimation).
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Soumis le : lundi 21 novembre 2016 - 15:20:04
Dernière modification le : mardi 30 janvier 2018 - 17:50:04
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  • HAL Id : halshs-01400186, version 1



Bertrand K. Hassani, Wei Yang. The Lila distribution and its applications in risk modelling. Documents de travail du Centre d'Economie de la Sorbonne 2016.68 - ISSN : 1955-611X. 2016. 〈halshs-01400186〉



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