Multivariate distributions with support above the diagonal

Abstract

A general family of distributions for the empirical modelling of ordered multivariate data is proposed. The family is based on, but greatly extends, the joint distribution of order statistics from an independent and identically distributed univariate sample. General properties, including marginal and conditional distributions, bivariate dependence, limiting distributions and links to the Dirichlet distribution are described. Univariate and bivariate special cases of the multivariate distributions, the latter including an equivalent rotated version, are considered. Two particular tractable special cases are stressed. The models are successfully and usefully fitted, by maximum likelihood, to meteorological data. The models are also applicable to data in which one variable is unconstrained and the other are all nonnegative.