Parameter Dependence in Stochastic Modeling—Multivariate Distributions

• 作者: Jerzy K. Filus Lidia Z. Filus
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: MULTIVARIATE Probability DISTRIBUTIONS Stochastic DEPENDENCE Paradigms MULTIVARIATE Gaussian DISTRIBUTIONS PARAMETER DEPENDENCE Method of Construction CONDITIONING Stress BIOMEDICAL Applications
• 年，卷（期）: 2014,（6）
• 页码范围: 928-940
• 页数: 13页
• 分类号: O1

摘要

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.