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BY 4.0 license Open Access Published by De Gruyter Open Access October 1, 2020

The de Finetti structure behind some norm-symmetric multivariate densities with exponential decay

  • Jan-Frederik Mai EMAIL logo
From the journal Dependence Modeling


We derive a sufficient condition on the symmetric norm ||·|| such that the probability distribution associated with the density function f (x) ∝exp(−λ ||x||) is conditionally independent and identically distributed in the sense of de Finetti’s seminal theorem. The criterion is mild enough to comprise the p-norms as special cases, in which f is shown to correspond to a polynomially tilted stable mixture of products of transformed Gamma densities. In another special case of interest f equals the density of a time-homogeneous load sharing model, popular in reliability theory, whose motivation is a priori unrelated to the concept of conditional independence. The de Finetti structure reveals a surprising link between time-homogeneous load sharing models and the concept of Lévy subordinators.

MSC 2010: 62H05; 60E07


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Received: 2020-05-25
Accepted: 2020-09-02
Published Online: 2020-10-01

© 2020 Jan-Frederik Mai, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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