Open Access
August 2013 Construction of multivariate dispersion models
Bent Jørgensen
Braz. J. Probab. Stat. 27(3): 285-309 (August 2013). DOI: 10.1214/11-BJPS171


We consider methods for constructing multivariate dispersion models, illustrated by examples. Such methods are motivated by the need for good regression modelling of multivariate nonnormal correlated data, which requires multivariate distributions with a flexible correlation structure. We first review existing methods for constructing multivariate proper dispersion models, involving quadratic forms of deviance residuals in the style of the multivariate normal density, which we illustrate by a multivariate hyperbola distribution. We develop an extended convolution method for constructing multivariate exponential dispersion models, designed to create a fully flexible covariance structure, which we illustrate by two bivariate gamma distributions. We develop a similar technique for constructing multivariate extreme dispersion models for extremes and survival data, and introduce new bivariate logistic and Gumbel distributions.


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Bent Jørgensen. "Construction of multivariate dispersion models." Braz. J. Probab. Stat. 27 (3) 285 - 309, August 2013.


Published: August 2013
First available in Project Euclid: 28 May 2013

zbMATH: 1298.62108
MathSciNet: MR3064725
Digital Object Identifier: 10.1214/11-BJPS171

Keywords: Convolution method , multivariate exponential dispersion model , multivariate extreme dispersion model , multivariate proper dispersion model

Rights: Copyright © 2013 Brazilian Statistical Association

Vol.27 • No. 3 • August 2013
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