Multiplicative strong unimodality for positive stable laws
Thomas Simon (LPP)
TL;DR
This paper investigates the multiplicative strong unimodality of positive stable laws, establishing that such laws are multiplicative strongly unimodal if and only if their stability parameter is less than or equal to 1/2.
Contribution
It provides a complete characterization of the multiplicative strong unimodality for positive stable laws based on their stability parameter.
Findings
Positive alpha-stable laws are multiplicative strongly unimodal iff alpha ≤ 1/2.
The result completes the understanding of unimodality properties for stable distributions.
The paper clarifies the conditions under which positive stable laws exhibit multiplicative strong unimodality.
Abstract
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 stable laws are multiplicative strongly unimodal iff
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Probability and Risk Models · Stochastic processes and financial applications