A b s t r a c t . We give a general result to characterize a multivariate distribution from a relationship between the left truncated mean function and the hazard gradient function. This result allows us to obtain new characterizations of multivariate distributions. In particular, we show that, for the multivariate normal distribution, the simple relationship, obtained in standardized form by M...

Copulas are statistical tools for modelling the multivariate structure between variables in a distribution free way. They are beginning to be used in financial literature as an alternative to the multivariate normal. After reviewing the main properties of bivariate and multivariate copulas, three multivariate families are presented: the classical multivariate normal, the Fairlie-Gumbel-Morganst...

Deheuvels [J. Multivariate Anal. 11 (1981) 102–113] and Genest and Rémillard [Test 13 (2004) 335–369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramér–von Mises statistics derived from a Möbius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous seq...

The theory of the goodness of fit procedures for multivariate normality based on spherical harmonics, introduced in [6], is extended to cover the context of the multivariate linear model (MLM). The limiting distribution of the statistics considered does depend on the distribution of the covariates in the MLM, and our results provide a complete description of the manner in which the covariate di...

This paper presents the conditions for robustness to the nonnormality on three test statistics for a general multivariate linear hypothesis, which were proposed under the normal assumption in a generalized multivariate analysis of variance (GMANOVA) model. The proposed conditions require the cumulants of an unknown population’s distribution to vanish in the second terms of the asymptotic expans...