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Multiplicative Strong Unimodality

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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.
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Keywords: dispersive order; gamma distribution; mixture; star order; strong unimodality; unimodality

Document Type: Original Article

Affiliations: 1: Universitatea Bucuresti, 2: Université Laval

Publication date: June 1, 1998

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