Bivariate Kurtotic Distributions of Garment Fibre Data

Abstract

A bivariate and unimodal distribution is introduced to model an unconventionally distributed data set collected by the Forensic Science Service. This family of distributions allows for a different kurtosis in each orthogonal direction and has a constructive rather than probability density function definition, making conventional inference impossible. However, the construction and inference work well with a Bayesian Markov chain Monte Carlo analysis. Copyright 2003 Royal Statistical Society.

Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers

“…In this article, we restrict the set of transformations by imposing that for any distribution there is one set of orthogonal coordinates along which the components are independent and have known univariate distributions. In the (rather different) context of bivariate symmetric distributions with different kurtosis, Hoggart et al (2003) introduced a class of distributions with a similar characteristic.…”