4. Multivariate Distributions

1. Catherine Forbes1,
2. Merran Evans1,
3. Nicholas Hastings2 and
4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch4

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Multivariate Distributions, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch4

Author Information

1. 1

Monash University, Victoria, Australia

2. 2

Albany Interactive, Victoria, Australia

3. 3

Brian Peacock Ergonomics, SIM University, Singapore

Publication History

1. Published Online: 16 DEC 2010
2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242

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Keywords:

• Bayes’ theorem;
• conditional distributions;
• independence;
• joint probability;
• marginal distribution;
• multivariate distributions;
• probability density function

Summary

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