Multiplicative strong unimodality for positive stable laws

Simon, Thomas

doi:10.1090/S0002-9939-2010-10697-4

Multiplicative strong unimodality for positive stable laws
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Proc. Amer. Math. Soc. 139 (2011), 2587-2595 Request permission

Abstract:

It is known that real non-Gaussian stable laws are unimodal, not additive strongly unimodal, multiplicative strongly unimodal in the symmetric case, and that the only remaining relevant situation for the multiplicative strong unimodality is the one-sided case. It is shown here that positive $\alpha$-stable distributions are multiplicative strongly unimodal if and only if $\alpha \le 1/2.$

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