A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On Boolean selfdecomposable distributions

Volume 274 / 2024

Takahiro Hasebe, Kei Noba, Noriyoshi Sakuma, Yuki Ueda Studia Mathematica 274 (2024), 129-151 MSC: Primary 46L54; Secondary 60E07 DOI: 10.4064/sm221227-29-10 Published online: 24 January 2024

Abstract

This paper introduces the class of selfdecomposable distributions concerning Boolean convolution. A general regularity property of Boolean selfdecomposable distributions is established; in particular, the number of atoms is at most 2 and the singular continuous part is 0. We then analyze how shifting probability measures changes Boolean selfdecomposability. Several examples are presented to supplement the above results. Finally, we prove that the standard normal distribution $N(0,1)$ is Boolean selfdecomposable but the shifted one $N(m,1)$ is not for sufficiently large $|m|$.

Authors

  • Takahiro HasebeDepartment of Mathematics
    Hokkaido University
    Sapporo, 060-0810 Hokkaido, Japan
    e-mail
  • Kei NobaDepartment of Statistical Inference and Mathematics
    The Institute of Statistical Mathematics
    Tachikawa, 190-8562 Tokyo, Japan
    e-mail
  • Noriyoshi SakumaGraduate School of Natural Sciences
    Nagoya City University
    Nagoya, 467-8501 Aichi, Japan
    e-mail
  • Yuki UedaDepartment of Mathematics
    Hokkaido University of Education
    Asahikawa, 070-8621 Hokkaido, Japan
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image