Minimal symmetrization of random vectors in \(R^2\). (English. Ukrainian original) Zbl 0995.60009

Turbin, A. F.; Samojlenko, I. V.

Theory Probab. Math. Stat. 62, 165-170 (2001); translation from Teor. Jmovirn. Mat. Stat. 62, 151-156 (2000).

It is known that a random variable \(\xi\) has a symmetric distribution if \(\xi\) and \(-\xi\) are identically distributed. If \(\xi_{1}\) and \(\xi_{2}\) are identically distributed (independence is not supposed), then the random variable \(\xi=\xi_{1}-\xi_{2}\) has a symmetric distribution. The aim of this paper is to extend the above-mentioned property to random vectors with values in \(n\)-measurable Euclidean space \(R^{n},\) \(n\geq 2.\) The properties of symmetrized vectors and analogues of the famous symmetric distributions are studied.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60B11	Probability theory on linear topological spaces
33C10	Bessel and Airy functions, cylinder functions, \({}_0F_1\)
60E05	Probability distributions: general theory

Keywords:

random vectors in \(R^{2}\); minimal symmetrization