Statistical Science

Conditionally Specified Distributions: An Introduction (with comments and a rejoinder by the authors)

Barry C. Arnold, Enrique Castillo, and José María Sarabia

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Abstract

A bivariate distribution can sometimes be characterized completely by properties of its conditional distributions. The present article surveys available research in this area. Questions of compatibility of conditional specifications are addressed as are characterizations of distributions based on their having conditional distributions that are members of prescribed parametric families of distributions. The topics of compatibility and near compatibility of conditional distributions are discussed. Estimation strategies for conditionally specified distributions are summarized. Additionally, certain conditionally specified densities are shown to provide convenient flexible conjugate prior families in certain multi- parameter Bayesian settings.

Article information

Source
Statist. Sci. Volume 16, Issue 3 (2001), 249-274.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.ss/1009213728

Digital Object Identifier
doi:10.1214/ss/1009213728

Mathematical Reviews number (MathSciNet)
MR1874154

Zentralblatt MATH identifier
1059.62511

Keywords
Compatibility near-compatibility normal conditionals conjugate priors functional equations exponential families

Citation

Arnold, Barry C.; Castillo, Enrique; Sarabia, José María. Conditionally Specified Distributions: An Introduction (with comments and a rejoinder by the authors). Statist. Sci. 16 (2001), no. 3, 249--274. doi:10.1214/ss/1009213728. https://projecteuclid.org/euclid.ss/1009213728.


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