  We propose and study the class of Box-Cox elliptical distributions. It
provides alternative distributions for modeling multivariate positive,
marginally skewed and possibly heavy-tailed data. This new class of
distributions has as a special case the class of log-elliptical distributions,
and reduces to the Box-Cox symmetric class of distributions in the univariate
setting. The parameters are interpretable in terms of quantiles and relative
dispersions of the marginal distributions and of associations between pairs of
variables. The relation between the scale parameters and quantiles makes the
Box-Cox elliptical distributions attractive for regression modeling purposes.
Applications to data on vitamin intake are presented and discussed.
