Multivariate discrete distributions via sums and shares

Jones, M. C.; Marchand, Éric

doi:10.1016/j.jmva.2018.11.011

Cited by 12 publications

(3 citation statements)

References 21 publications

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“…for β 1 , β 2 > 0 and β 1 + β 2 < 1. Appell's F 1 function appears in a similar way, again in a Bayesian framework, as a bivariate discrete distribution called Bailey by Laurent (2012) (see also Jones & Marchand, 2019 for another derivation). For the particular case a i = ν i /2, i = 1, 2, the p.m.f.…”

Section: Type I Mixturesmentioning

confidence: 96%

Bayesian estimation and prediction for certain mixtures

LMoudden,

Marchand

2020

Preprint

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For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as Kibble-type, non-central Chi-square and F distributions, the distribution of R 2 in multiple regression, variance mixture of normal distributions, and mixtures of location-scale exponential distributions including the multivariate Lomax distribution. An emphasis is also placed on analytical representations and the relationships with a host of existing distributions and several hypergeomtric functions of one or two variables.

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Section: Type I Mixturesmentioning

confidence: 96%

Bayesian estimation and prediction for certain mixtures

LMoudden,

Marchand

2020

Preprint

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“…, X m,n m with finite means gives us the convergence result (23); see, e.g., [10]. Now, to obtain the representation ( 22), we insert the expression (15) of S into formula (13). This yields, for all k j ∈ {1, .…”

Section: Mixed Geometric Model As a Limitmentioning

confidence: 99%

“…Castañer and Claramunt [5] discussed the link with equilibrium distributions. Jones and Marchand [13] developed a generalized model based on a sum and share decomposition.…”

Section: Introductionmentioning

confidence: 99%

Partially Schur-constant models

Castañer

Bielsa

Lefèvre

et al. 2019

Journal of Multivariate Analysis

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In this paper, we introduce a new multivariate dependence model that generalizes the standard Schur-constant model. The difference is that the random vector considered is partially exchangeable, instead of exchangeable, whence the term partially Schur-constant. Its advantage is to allow some heterogeneity of marginal distributions and a more flexible dependence structure, which broadens the scope of potential applications. We first show that the associated joint survival function is a monotonic multivariate function. Next, we derive two distributional representations that provide an intuitive understanding of the underlying dependence. Several other properties are obtained, including correlations within and between subvectors. As an illustration, we explain how such a model could be applied to risk management for insurance networks.

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