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

Mai Jan-Frederik ()
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Mai Jan-Frederik: XAIA Investment GmbH, Sonnenstr. 19, 80331München

Dependence Modeling, 2020, vol. 8, issue 1, 210-220

Abstract: 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 ℓp-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.

Keywords: infinite divisibility; Lévy subordinator; de Finetti’s theorem; exchangeability; min-stable multi-variate exponential distribution (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:8:y:2020:i:1:p:210-220:n:9

DOI: 10.1515/demo-2020-0012

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