STATISTICAL INFERENCE FOR A GENERAL CLASS OF NONCENTRAL ELLIPTICAL DISTRIBUTIONS

In this paper we introduce a new family of noncentral elliptical distributions. This family is generated as the quotient of two independent random variables, one with noncentral standard elliptical distribution and the other the power of a U(0, 1) random variable. For this family of distributions, we derive general properties, including the moments and discuss some special cases based on the family of scale mixtures of normal distributions, where the main advantage is easy simulation and nice hierarchical representation facilitating the implementation of an EM algorithm for maximum likelihood estimation. This new family of distributions provides a robust alternative for parameter estimation in asymmetric distributions. The results and methods are applied to three real datasets, showing that this new distribution fits better than other models reported in the recent statistical literature.

Automated summary

In this paper, a new family of noncentral elliptical distributions is introduced, generated as the quotient of two independent random variables. General properties, including moments, as well as special cases are derived, showing the advantages of this distribution family in parameter estimation. The results and methods are applied to real datasets, demonstrating better fit compared to other models in recent statistical literature.