Multivariate Distributions
Catherine Scipione Forbes, Merran Evans, Nicholas Anthony John Hastings, Brian Peacock · 2010
Joint probability statements can be made about a combination of variates, all having continuous domain, all having countable domain, or some combination of continuous and countable domains. Probabilities associated with a univariate element of a bivariate without regard to the value of the other univariate element within the same bivariate arise from the marginal distribution of that univariate. Corresponding to such a marginal distribution are the range, quantile, and probability domain associated with the univariate element, with each one consistent with the corresponding bivariate entity. Two univariates are said to be independent if the marginal probabilities associated with the outcomes of one variate are not influenced by the observed value of the other variate, and vice versa. The chapter also discusses conditional distributions, Bayes’ theorem and functions of a multivariate. Controlled Vocabulary Terms conditional probability distribution; joint probability; marginal distribution; multivariate statistics; probability density function