[4] (This definition is not equivalent to Mardia's bivariate Pareto distribution of the second kind.
)[3] For a > 1, the marginal means are while for a > 2, the variances, covariance, and correlation are the same as for multivariate Pareto of the first kind.
The complementary CDF is The marginal means and variances are given by If a > 2 the covariances and correlations are positive with Arnold[4] suggests representing the multivariate Pareto Type I complementary CDF by If the location and scale parameter are allowed to differ, the complementary CDF is which has marginal distributions of the same type (3) and Pareto Type II univariate marginal distributions.
[4] For a > 1, the marginal means are while for a > 2, the variances, covariances, and correlations are the same as for multivariate Pareto of the first kind.
A random vector X has a k-dimensional Feller–Pareto distribution if where are independent gamma variables.