A1137
Title: Extremal negative dependence and the strongly Rayleigh property-part B
Authors: Helene Cossette - Laval University (Canada)
Etienne Marceau - Laval University (Canada)
Alessandro Mutti - Politecnico di Torino (Italy) [presenting]
Patrizia Semeraro - Politecnico di Torino (Italy)
Abstract: Multivariate Bernoulli distributions are essential in the modeling of binary data in a wide variety of contexts, such as actuarial science, quantitative risk management, machine learning, natural language processing, and bioinformatics. The aim is to present the second part of the investigation about extremal negative dependence for Bernoulli random vectors and the strongly Rayleigh property. The strongly Rayleigh property is the strongest negative dependence notion, implying negative association. The strongly Rayleigh property is often defined using the probability generating function of the Bernoulli random vector. Notably, a Bernoulli random vector satisfies the strongly Rayleigh property if its probability generating function is a stable polynomial. Methods to construct families of multivariate Bernoulli distributions that satisfy both the strongly Rayleigh property and the Sigma-countermonotonicity property (discussed in the first part of the investigation) are presented. Those notions are explained using the class of conditional Bernoulli distributions. Both the strongly Rayleigh property and the Sigma-countermonotonicity property are illustrated through examples in actuarial science and risk management.
