The Annals of Probability

Convolution of Unimodal Distributions Can Produce any Number of Modes

Ken-Iti Sato

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Abstract

For any positive integer $n$, there exists a unimodal distribution $\mu$ such that $\mu \ast \mu$ is $n$-modal. Furthermore, there is a unimodal distribution $\mu$ such that $\mu \ast \mu$ has infinitely many modes. Lattice analogues of the results are also given.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1543-1549.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989129

Digital Object Identifier
doi:10.1214/aop/1176989129

Mathematical Reviews number (MathSciNet)
MR1235427

Zentralblatt MATH identifier
0788.60024

JSTOR
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory

Keywords
Unimodal $n$-modal $\infty$-modal convolution modes bottoms

Citation

Sato, Ken-Iti. Convolution of Unimodal Distributions Can Produce any Number of Modes. Ann. Probab. 21 (1993), no. 3, 1543--1549. doi:10.1214/aop/1176989129. https://projecteuclid.org/euclid.aop/1176989129


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