Multiplicative strong unimodality for positive stable laws

Thomas Simon (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation for the multiplicative strong unimodality of stable laws is the one-sided. In this paper, we show that positive $\alpha-$stable laws are multiplicative strongly unimodal iff $\alpha\le 1/2.$

Mots clés: Beta and Gamma variables; Log-concavity; Positive stable law; Strong unimodality

Domaines: Probabilités [math.PR]

Thomas Simon. Multiplicative strong unimodality for positive stable laws. 2010. ⟨hal-00460134⟩