Multivariate distributions with generalized inverse gaussian marginals, and associated poisson mixtures

Barndorff–Nielsen, Ole E.; Blæsild, P.; Seshadri, V.

doi:10.2307/3315462

Cited by 30 publications

(19 citation statements)

References 22 publications

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“…Their model assumes two independent Poisson distributions with parameters jointly distributed according to the bivariate inverse Gaussian distribution. Barndorff-Nielsen et al (1992) extended this model to the case of multivariate Poisson-multivariate generalized inverse Gaussian distributions. Xekalaki (1984b) demonstrated various models leading to the bivariate generalized Waring distribution.…”

Section: Mixed Bivariate Poisson Distributions Of the 2nd Kindmentioning

confidence: 97%

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Mixed Poisson Distributions

Karlis

Xekalaki

2007

International Statistical Review

270

209

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Mixed Poisson distributions have been used in a wide range of scientific fields for modeling nonhomogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential information on general mixtures. A selective presentation of some of the most prominent members of the family of Poisson mixtures is made.

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Section: Mixed Bivariate Poisson Distributions Of the 2nd Kindmentioning

confidence: 97%

“…Their model assumes two independent Poisson distributions with parameters jointly distributed according to the bivariate inverse Gaussian distribution. Barndorff-Nielsen et al (1992)…”

Section: Mixed Bivariate Poisson Distributions Of the 2nd Kindmentioning

confidence: 99%

Mixed Poisson Distributions

Karlis

Xekalaki

2007

International Statistical Review

270

209

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“…The process we are going to introduce could be an alternative to the multidimensional GH process. The multivariate generalized hyperbolic distribution (MGH) is defined in the literature as a normal mean-variance distribution with mixing variable GIG distributed: see Barndorff-Nielsen [2], [6] and Barndorff-Nielsen at al. [7].…”

Section: The Multivariate Gh Modelmentioning

confidence: 99%

“…The above argument supports our choice of a one factor structure for the change of time. The construction is therefore based on a random-additive-effect model, as introduced in Barndorff-Nielsen et al [6]. The one factor change of time has been used in Semeraro [25] and Luciano and Semeraro [19] to generalize the multivariate variance gamma and other processes of interest in Finance.…”

Section: Introductionmentioning

confidence: 99%

A Generalized Normal Mean-Variance Mixture for Return Processes in Finance

Luciano

Semeraro

2010

Int. J. Theor. Appl. Finan.

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Time-changed Brownian motions are extensively applied as mathematical models for asset returns in Finance. Time change is interpreted as a switch to trade-related business time, different from calendar time. Time-changed Brownian motions can be generated by infinite divisible normal mixtures. The standard multivariate normal mean variance mixtures assume a common mixing variable. This corresponds to a multidimensional return process with a unique change of time for all assets under exam. The economic counterpart is uniqueness of trade or business time, which is not in line with empirical evidence.In this paper we propose a new multivariate definition of normal mean-variance mixtures with a flexible dependence structure, based on the economic intuition of both a common and an idiosyncratic component of business time. We analyze both the distribution and the related process.We use the above construction to introduce a multivariate generalized hyperbolic process with generalized hyperbolic margins. We conclude with a stock market example to show the ease of calibration of the model.

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“…Alternative multivariate distributions generated by a mixing process were considered by Barndorff-Nielsen et al (1992) and Gómez-Déniz et al (2008), among others.…”

Section: Multivariate Poisson-beta Distributionmentioning

confidence: 99%

Multivariate Poisson-Beta Distributions with Applications

Sarabia

Gómez–Déniz

2011

Communications in Statistics - Theory and Methods

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In this article we propose multivariate versions of the beta mixture of Poisson distribution considered by Gurland (1958), Katti (1966), andHolla andBhattacharya (1965). The new class of distributions can be used for modeling multivariate dependent count data when marginal overdispersion is observed. After revising briefly some of their properties, a general multivariate model with Poisson-Beta marginals and with a flexible covariance structure is proposed. Several specific models as well as a model which admits correlations of any sign are considered. Estimation methods are discussed. Finally, examples of application for bivariate frequencies data are given.

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Multivariate distributions with generalized inverse gaussian marginals, and associated poisson mixtures

Cited by 30 publications

References 22 publications

Mixed Poisson Distributions

Mixed Poisson Distributions

A Generalized Normal Mean-Variance Mixture for Return Processes in Finance

Multivariate Poisson-Beta Distributions with Applications

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