Jerzy K. Filus, Lidia Z. Filus

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Department of Mathematics and Computer Science, Oakton Community College, Des Plaines, USA.
Department of Mathematics, Northeastern Illinois University, Chicago, USA.
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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.

Keywords: Multivariate Probability Distributions, Stochastic Dependence Paradigms, Multivariate Gaussian Distributions, Parameter Dependence Method of Construction, Conditioning, Stress, Biomedical Applications

Cite this paper: Filus, J. and Filus, L. (2014) Parameter Dependence in Stochastic Modeling—Multivariate Distributions. Applied Mathematics, 5, 928-940. doi: 10.4236/am.2014.56088.

References

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