Power means of random variables and characterizations of distributions via fractional calculus

• Autorzy: Okamura Kazuki , Otobe Yoshiki

Identyfikatory

DOI

10.37190/0208-4147.00175

• Języki publikacji: EN

Abstrakty

EN

We investigate fractional moments and expectations of power means of complex-valued random variables by using fractional calculus. We deal with both negative and positive orders of the fractional derivatives. The one-dimensional distributions are characterized in terms of the fractional moments without any moment assumptions. We explicitly compute the expectations of the power means for both the univariate Cauchy distribution and the Poincaré distribution on the upper half-plane. We show that for these distributions the expectations are invariant with respect to the sample size and the value of the power.

Słowa kluczowe

EN

fractional moments; power mean; characterization of distribution; Cauchy distribution; Poincaré distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2024
• Tom: Vol. 44, Fasc. 1
• Strony: 133--156
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Okamura Kazuki

• Department of Mathematics Shizuoka University Shizuoka city, Shizuoka, Japan

autor

Otobe Yoshiki

• Department of Mathematics Shinshu University Matsumoto city, Nagano, Japan

Bibliografia

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