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Multiplicative Strong Unimodality
Author(s) -
Cuculescu Ioan,
Theodorescu Radu
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00023
Subject(s) - unimodality , mathematics , multiplicative function , combinatorics , mathematical analysis
Multiplicative strong unimodality is defined as the preservation of unimodality in products of independent random variables. An Ibragimov type theorem is proved. As an application, preserving unimodality for scale mixtures of gamma distributions is examined. It is also shown that multiplicative strong unimodal probability measures on R appear as images, by the exponential map, of classical strong unimodal ones. The connection to the star order is also established.