The Lukacs-Olkin-Rubin theorem on symmetric cones without invariance of the "quotient"

Abstract

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, Ann. Math. Stat. 33 (1962), 1272--1280]. 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, the new proof of the Olkin--Baker functional equation on symmetric cones is given.

arXiv comment14 pages. arXiv admin note: text overlap with arXiv:1206.6091, arXiv:1307.3988

References in corpus (3)

• The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem
• Extension of the Olkin and Rubin Characterization to the Wishart distribution on homogeneous cones
• Multiplicative Cauchy functional equation on symmetric cones

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