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Convolutions of α‐unimodal discrete distributions
Author(s) -
Wu F.,
Dharmadhikari S.
Publication year - 1999
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00108
Subject(s) - unimodality , mathematics , convolution (computer science) , distribution (mathematics) , combinatorics , mathematical analysis , computer science , artificial intelligence , artificial neural network
This note proves that the convolution of an α‐unimodal discrete distribution with a β‐unimodal discrete distribution is (α+β)‐unimodal whenever (α+β)≥1. This is the discrete analogue of the fundamental result on generalized unimodality given by Olshen and Savage (1970).