Free Infinite Divisibility for Generalized Power Distributions with Free Poisson Term

• Autorzy: Morishita Junki , Ueda Yuki

Identyfikatory

DOI

10.37190/0208-4147.40.2.4

• Języki publikacji: EN

Abstrakty

EN

We study free infinite divisibility (FID) for a class of generalized power distributions with free Poisson term by using complex analytic methods and free cumulants. In particular, we prove that (i) if X follows the free generalized inverse Gaussian distribution, then the distribution of X^r is FID when │r│≥1; (ii) if S follows the standard semicircle law and u > 2, then the distribution of (S + u)^r is FID when r≤−1; (iii) if B_p follows the beta distribution with parameters p and 3/2, then (iii-a) the distribution of B^r_p is FID when │r│≥1 and 0 < p≤1/2; (iii-b) the distribution of B^r_p is FID when r≤−1 and p >1/2.

Słowa kluczowe

EN

free infinite divisibility; univalent inverse Cauchy transform; free cumulant; powers of random variables

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 2
• Strony: 245--267
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Morishita Junki

• Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan

autor

Ueda Yuki

• Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).