The multivariate asymmetric slash Laplace distribution and its applications

Abstract

We have introduced a multivariate asymmetric-slash Laplace distribution, a flexible distribution that can take skewness and heavy tails into account. This distribution is useful in simulation studies where it can introduce distributional challenges in order to evaluate a statistical procedure. It is also useful in analyzing data sets that do not follow the normal law. We have used the microarray data set for illustration. The asymmetric slash Laplace distribution provides the possibility of modelling impulsiveness and skewness required for gene expression data. Hence, the probability distribution presented in this paper will be very useful in estimation and detection problems involving gene expression data. The multivariate asymmetric-slash Laplace distribution introduced in this article is clearly an alternative to multivariate skew-slash distributions because it can model skewness, peakedness and heavy tails. One interesting advantage of the multivariate asymmetric slash Laplace distribution is that its moments can be computed analytically by taking advantage of the moments of the multivariate asymmetric Laplace distribution, see the discussion in Section 3. Another attractive feature is that simulations from the multivariate asymmetric-slash Laplace distribution are straightforward from softwares that permit simulations from the multivariate asymmetric Laplace or Laplace distribution. We believe that the new class will be useful for analyzing data sets having skewness and heavy tails. Heavy-tailed distributions are commonly found in complex multi-component systems like ecological systems, biometry, economics, sociology, internet traffic, finance, business etc.