Boolean Extremes and Dagum Distributions

2017/11/16 by Vargas, Jorge Garza, Voiculescu, Dan-Virgil
#46L53 #60G70 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.06227

Abstract

We study the max-convolution and max-stable laws for Boolean independence and prove that these are Dagum distributions (also known as log-logistical distributions).

Related

• Limit laws for boolean convolutions
• On the rate of convergence to the Boolean extreme value distribution under the von Mises condition
• Unimodality of Boolean and monotone stable distributions
• Conditional independence among max-stable laws
• Limit theorems for monotonic convolution and the Chernoff product formula