Elliptically symmetric distributions
IEEE Transactions on Information Theory
Operator geometric stable laws
Journal of Multivariate Analysis
Approximating the distributions of estimators of financial risk under an asymmetric Laplace law
Computational Statistics & Data Analysis
Goodness-of-fit tests for multivariate Laplace distributions
Mathematical and Computer Modelling: An International Journal
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Asymmetric Laplace laws form a subclass of geometric stable distributions, the limiting laws in the random summation scheme with a geometric number of terms. Among geometric stable laws, they play a role analogous to that of normal distribution among stable Paretian laws. However, with steeper peaks and heavier tails than normal distribution, asymmetric Laplace laws reflect properties of empirical financial data sets much better than the normal model. Despite heavier than normal tails, they have finite moments of any order. In addition, explicit analytical forms of their one-dimensional densities and convenient computational forms of their multivariate densities make estimation procedures practical and relatively easy to implement. Thus, asymmetric Laplace laws provide and interesting, efficient, and user friendly alternative to normal and stable Paretian distributions for modeling financial data. We present an overview of the theory of asymmetric Laplace laws and their applications in modeling currency exchange rates.