A Class of Multivariate Max-Infinitely Divisible Distributions Based on Random Scaling

A class of exchangeable multivariate max-id distributions with 1-norm pound symmetric exponent measure was introduced by Genest, Neslehova and Rivest in a paper published in the journal Bernoulli in 2018. Three years later, an extended class of exchangeable multivariate max-id distributions with p-norm pound symmetric exponent measure was proposed by Mai and Wang in an article which appeared in the Journal of Multivariate Analysis. A new class is proposed here which encompasses them both and which allows for non-exchangeability, thereby providing extra flexibility for modeling multivariate block maxima data and extreme risks. Some properties of members of this class are studied, and conditions are given under which they are multivariate extreme-value distributions. The maximum attractor of each class member is also determined under broad conditions, and an algorithm due to Jan-Frederik Mai is adapted for simulation purposes.