Convolution of Unimodal Distributions Can Produce any Number of Modes
Sato, Ken-Iti
Ann. Probab., Tome 21 (1993) no. 4, p. 1543-1549 / Harvested from Project Euclid
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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.
Publié le : 1993-07-14
Classification:  Unimodal,  $n$-modal,  $\infty$-modal,  convolution,  modes,  bottoms,  60E05 
@article{1176989129,
     author = {Sato, Ken-Iti},
     title = {Convolution of Unimodal Distributions Can Produce any Number of Modes},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 1543-1549},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989129}
}

Sato, Ken-Iti. Convolution of Unimodal Distributions Can Produce any Number of Modes. Ann. Probab., Tome 21 (1993) no. 4, pp.  1543-1549. http://gdmltest.u-ga.fr/item/1176989129/