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On free and classical type G distributions

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Standard

On free and classical type G distributions. / Arizmendi, Octavio; Barndorff-Nielsen, Ole Eiler; Pérez-Abreu, Víctor.

I: Brazilian Journal of Probability and Statistics, Bind 24, Nr. 2, 2010, s. 106-127.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Harvard

Arizmendi, O, Barndorff-Nielsen, OE & Pérez-Abreu, V 2010, 'On free and classical type G distributions', Brazilian Journal of Probability and Statistics, bind 24, nr. 2, s. 106-127. https://doi.org/10.1214/09-BJPS039

APA

Arizmendi, O., Barndorff-Nielsen, O. E., & Pérez-Abreu, V. (2010). On free and classical type G distributions. Brazilian Journal of Probability and Statistics, 24(2), 106-127. https://doi.org/10.1214/09-BJPS039

CBE

Arizmendi O, Barndorff-Nielsen OE, Pérez-Abreu V. 2010. On free and classical type G distributions. Brazilian Journal of Probability and Statistics. 24(2):106-127. https://doi.org/10.1214/09-BJPS039

MLA

Arizmendi, Octavio, Ole Eiler Barndorff-Nielsen og Víctor Pérez-Abreu. "On free and classical type G distributions". Brazilian Journal of Probability and Statistics. 2010, 24(2). 106-127. https://doi.org/10.1214/09-BJPS039

Vancouver

Arizmendi O, Barndorff-Nielsen OE, Pérez-Abreu V. On free and classical type G distributions. Brazilian Journal of Probability and Statistics. 2010;24(2):106-127. https://doi.org/10.1214/09-BJPS039

Author

Arizmendi, Octavio ; Barndorff-Nielsen, Ole Eiler ; Pérez-Abreu, Víctor. / On free and classical type G distributions. I: Brazilian Journal of Probability and Statistics. 2010 ; Bind 24, Nr. 2. s. 106-127.

Bibtex

@article{0013e7a005dd11dfb95d000ea68e967b,
title = "On free and classical type G distributions",
abstract = "There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type G distributions. A new characterization of classical type G distributions is given first and the class of type A classical infinitely divisible distributions is introduced. The corresponding free type A distributions are studied and the role of a special symmetric beta distribution is shown as a building block for free type A distributions. It is proved that this symmetric beta distribution is the free multiplicative convolution of an arcsine distribution with the Marchenko–Pastur distribution.",
author = "Octavio Arizmendi and Barndorff-Nielsen, {Ole Eiler} and V{\'i}ctor P{\'e}rez-Abreu",
year = "2010",
doi = "10.1214/09-BJPS039",
language = "English",
volume = "24",
pages = "106--127",
journal = "Brazilian Journal of Probability and Statistics",
issn = "0103-0752",
publisher = "Associacao Brasileira de Estatistica",
number = "2",

}

RIS

TY - JOUR

T1 - On free and classical type G distributions

AU - Arizmendi, Octavio

AU - Barndorff-Nielsen, Ole Eiler

AU - Pérez-Abreu, Víctor

PY - 2010

Y1 - 2010

N2 - There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type G distributions. A new characterization of classical type G distributions is given first and the class of type A classical infinitely divisible distributions is introduced. The corresponding free type A distributions are studied and the role of a special symmetric beta distribution is shown as a building block for free type A distributions. It is proved that this symmetric beta distribution is the free multiplicative convolution of an arcsine distribution with the Marchenko–Pastur distribution.

AB - There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type G distributions. A new characterization of classical type G distributions is given first and the class of type A classical infinitely divisible distributions is introduced. The corresponding free type A distributions are studied and the role of a special symmetric beta distribution is shown as a building block for free type A distributions. It is proved that this symmetric beta distribution is the free multiplicative convolution of an arcsine distribution with the Marchenko–Pastur distribution.

U2 - 10.1214/09-BJPS039

DO - 10.1214/09-BJPS039

M3 - Journal article

VL - 24

SP - 106

EP - 127

JO - Brazilian Journal of Probability and Statistics

JF - Brazilian Journal of Probability and Statistics

SN - 0103-0752

IS - 2

ER -