An extremal property of the generalized arcsine distribution

Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2013. An extremal property of the generalized arcsine distribution. Metrika 76 (3) , pp. 347-355. 10.1007/s00184-012-0391-y

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Abstract

The main result of the paper is the following characterization of the generalized arcsine density p γ (t) = t γ−1(1 − t) γ−1/B(γ, γ) with t∈(0,1) and γ∈(0,12)∪(12,1) : a r.v. ξ supported on [0, 1] has the generalized arcsine density p γ (t) if and only if E|ξ−x|1−2γ has the same value for almost all x∈(0,1) . Moreover, the measure with density p γ (t) is a unique minimizer (in the space of all probability measures μ supported on (0, 1)) of the double expectation (γ−12)E|ξ−ξ′|1−2γ , where ξ and ξ′ are independent random variables distributed according to the measure μ. These results extend recent results characterizing the standard arcsine density (the case γ=12 ).

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Generalized arcsine distribution, Bochner–Khinchine theorem, Correlated observations, Experimental design
Publisher:	Springer
ISSN:	0026-1335
Last Modified:	20 Oct 2022 07:48
URI:	https://orca.cardiff.ac.uk/id/eprint/26450

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