Nonetheless, we argue that invoking a hierarchy of size distribution corresponds to our fractal hypothesis.
In contrast to the selection of special model structures and reduced scenarios, as used in sections −, here, the time hierarchy of the distribution processes was deployed to reduce mathematical complexity.
Also, a model of intermittent trapping invoking a hierarchy of trap sizes distribution naturally leads us to considering the fractal organization of the nuclear space.
In this hierarchy of generalized Pareto distributions, the classical model will be called the Pareto (I) distribution.
Multivariate income distributions are also of interest and, in that arena, a hierarchy of multivariate Pareto distributions is available, paralleling and closely related to the univariate hierarchy.
More specifically, we assumed in the first stage of the hierarchy that the distribution of, after ilr- transformation, has a normal distribution on ℝ K − 1 [ 39] centered at ilr(θ ij ) with variance-covariance matrix Υ ij, that is, 1 where denotes the multivariate normal distribution in ℝ K − 1.
As the basic distribution in our hierarchy of generalized Pareto models we use the classical Pareto distribution, called here the Pareto (I) distribution.
In groups with linear dominance hierarchies, the distribution of the cost of feeding competition may be in part determined by rank, as high rank is often associated with greater feeding and foraging success and lower costs (Vehrencamp 1983).
Specifically, in the upper level of the hierarchy, distribution system operator uses market based control to coordinate the fleet operator׳s power schedule.
The first two of a hierarchy of equations for the multi-point distribution functions are derived by treating the random dislocation distributions and the corresponding stress fields in an ensemble average framework.
