The Open UniversitySkip to content

Multivariate discrete distributions via sums and shares

Jones, M. C. and Marchand, Éric (2019). Multivariate discrete distributions via sums and shares. Journal of Multivariate Analysis, 171 pp. 83–93.

Full text available as:
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (165kB) | Preview
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


In this article, we develop a sum and share decomposition to model multivariate discrete distributions, and more specifically multivariate count data that can be divided into a number of distinct categories. From a Poisson mixture model for the sum and a multinomial mixture model for the shares, a rich ensemble of properties, examples and relationships arises. As a main example, a seemingly new multivariate model involving a negative binomial sum and Polya shares is considered, previously seen only in the bivariate case, for which we present two contrasting applications. For other choices of the distribution of the sum, natural but novel discrete multivariate Liouville distributions emerge; an important special case of these is that of Schur constant distributions. Analogies and interactions with related continuous distributions are to the fore throughout.

Item Type: Journal Item
ISSN: 0047-259X
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 57794
Depositing User: M. C. Jones
Date Deposited: 20 Nov 2018 12:13
Last Modified: 26 Nov 2019 03:53
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU