The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”

Bartosz Kołodziejek


We prove the Lukacs–Olkin–Rubin theorem without invariance of the distribution of the “quotient,” which was the key assumption in the original proof of (Olkin–Rubin in Ann Math Stat 33:1272–1280, 1962). Instead, we assume existence of strictly positive continuous densities of respective random variables. We consider the (cone variate) “quotient” for any division algorithm satisfying some natural conditions. For that purpose, a new proof of the Olkin–Baker functional equation on symmetric cones is given.
Author Bartosz Kołodziejek (FMIS / DPMS)
Bartosz Kołodziejek,,
- Department of Probability and Mathematical Statistics
Journal seriesJournal of Theoretical Probability, ISSN 0894-9840
Issue year2016
Publication size in sheets0.9
Keywords in EnglishLukacs characterization, Division algorithm, Wishart distribution, Riesz distribution, Symmetric cones, Functional equations
ASJC Classification1804 Statistics, Probability and Uncertainty; 2600 General Mathematics; 2613 Statistics and Probability
Abstract in PolishW pracy uogólniono twierdzenie Lukacsa-Olkina-Rubina na przypadek stożków symetrycznych. Ponadto, osłabiono założenia regularnościowe na gęstości.
Languageen angielski
Score (nominal)20
Score sourcejournalList
ScoreMinisterial score = 15.0, 02-02-2020, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 02-02-2020, ArticleFromJournal
Publication indicators Scopus Citations = 4; WoS Citations = 5; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.976; WoS Impact Factor: 2016 = 0.854 (2) - 2016=0.8 (5)
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