Parameter Dependence in Stochastic Modeling—Multivariate Distributions

Abstract

We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bivariate normal case this dependence takes the form of a parameter (here the "expected value") of one probability density depending continuously (here linearly) on realizations of the other random variable. The point is, that such a pattern does not need to be restricted to that classical case of the bivariate normal. We show that this paradigm can be generalized and viewed in ways that allows one to extend it far beyond the bivariate or multivariate normal probability distributions class.

Two efficient heuristics to solve the integrated load distribution and production planning problem

“…In [19] the authors solve the optimal load distribution problem in which mission cost is minimized while satisfying the system reliability constraints. In [21] authors analyze the parameter dependency in stochastic modeling. The analysis provided in [21] can be applied in load optimization problem with system failure.…”

“…In [21] authors analyze the parameter dependency in stochastic modeling. The analysis provided in [21] can be applied in load optimization problem with system failure.…”