  Multivariate nonnegative orthant data are real vectors bounded to the left by
the null vector, and they can be continuous, discrete or mixed. We first review
the recent relative variability indexes for multivariate nonnegative continuous
and count distributions. As a prelude, the classification of two comparable
distributions having the same mean vector is done through under-, equi- and
over-variability with respect to the reference distribution. Multivariate
associated kernel estimators are then reviewed with new proposals that can
accommodate any nonnegative orthant dataset. We focus on bandwidth matrix
selections by adaptive and local Bayesian methods for semicontinuous and
counting supports, respectively. We finally introduce a flexible semiparametric
approach for estimating all these distributions on nonnegative supports. The
corresponding estimator is directed by a given parametric part, and a
nonparametric part which is a weight function to be estimated through
multivariate associated kernels. A diagnostic model is also discussed to make
an appropriate choice between the parametric, semiparametric and nonparametric
approaches. The retention of pure nonparametric means the inconvenience of
parametric part used in the modelization. Multivariate real data examples in
semicontinuous setup as reliability are gradually considered to illustrate the
proposed approach. Concluding remarks are made for extension to other multiple
functions.
