The Lila distribution and its applications in risk modelling

Bertrand K. Hassani () and Wei Yang ()
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Bertrand K. Hassani: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Wei Yang: Risk methodology - Grupo Santander

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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).

Keywords: probability distribution; parametric distribution; multimodal distribution; operational risk; market risk; pseudo bi-modal distribution (search for similar items in EconPapers)
Date: 2016-10
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01400186
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Citations: View citations in EconPapers (4)

Published in 2016

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