TITLE:
Parameter Dependence in Stochastic Modeling—Multivariate Distributions
AUTHORS:
Jerzy K. Filus, Lidia Z. Filus
KEYWORDS:
Multivariate Probability Distributions, Stochastic Dependence Paradigms, Multivariate Gaussian Distributions, Parameter Dependence Method of Construction, Conditioning, Stress, Biomedical Applications
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
8,
2014
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.