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A TRACTABLE SYMMETRIC MULTIVARIATE LOGISTIC DISTRIBUTION WITH BOUNDED SCORE FUNCTION

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  15 August 2025

PAUL G. BLACKWELL Open the ORCID record for PAUL G. BLACKWELL [Opens in a new window]
PAUL G. BLACKWELL*
Affiliation:
School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S3 7RH, UK
*
e-mail: p.blackwell@sheffield.ac.uk
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Abstract

Existing multivariate versions of the logistic probability distribution generally lack some of the useful properties of the univariate logistic distribution, such as its bounded score function or the tractability of its density function, or lack the rotational symmetry necessary for many applications. This paper clarifies some of the properties of such distributions and proposes a multivariate distribution closely related to the univariate logistic that has a tractable density, including the necessary normalising constant, bounded score function and elliptical symmetry. Some properties of its marginal distributions are explored, particularly in the bivariate case.

Keywords

multivariate logistic distributionbivariate distributionelliptical symmetry

MSC classification

Primary: 60E05: Distributions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 113 , Issue 2 , April 2026 , pp. 365 - 371
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author gratefully acknowledges the support of the Leverhulme Trust through Research Fellowship RF-2020-241.

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