Multiplicative Strong Unimodality

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 stro...

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Bibliographic Details
Published in:Australian & New Zealand journal of statistics 1998-06, Vol.40 (2), p.205-214
Main Authors: Cuculescu, Ioan, Theodorescu, Radu
Format: Article
Language:English
Subjects:
dispersive order
gamma distribution
mixture
star order
strong unimodality
unimodality
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Summary: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.
ISSN:1369-1473
1467-842X
DOI:10.1111/1467-842X.00023