A Method for Multivariate Probability Distributions Construction via Parameter Dependence

Abstract

The nature of stochastic dependence in the classic bivariate normal density framework is analyzed. In the case of this distribution we stress the way the conditional density of one of the random variables depends on realizations of the other. Typically, 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. Our point is that such a pattern does not need to be restricted to that classical case of bivariate normal. We show that this paradigm can be generalized and viewed in ways that allows us to extend it far beyond the bivariate normal distributions class.

Keywords:

• Bivariate normal density
• Conditioning
• Parameter dependence
• Reliability

Mathematics Subject Classification:

• Primary 62H05
• Secondary 62E10