期刊名称：Documents de Travail du Centre d'Economie de la Sorbonne
印刷版ISSN：1955-611X
出版年度：2016
出版社：Centre d'Economie de la Sorbonne
摘要：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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