2022/09/05 by Michela Corradini, Corradini, Michela, Kirstin Strokorb +1
Economics, Econometrics and Finance · Mathematics · #60E15 #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2209.02039
openalex publication_date 2022/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension d≥ 3 these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the Hüsler-Reiss family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the Hüsler-Reiss family this holds true even for the supermodular order.