Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of a specific type of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated by analyzing clusters consisting of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1993 to 2011.

A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach fully nonparametric. Although the analytical expression of the posterior is unknown, inference is possible via a trans-dimensional MCMC scheme. We show the efficiency of the proposed methodology by means of a simulation study. The extremal behaviour of log-returns of daily exchange rates between the Pound Sterling vs the U.S. Dollar and the Pound Sterling vs the Japanese Yen is analysed for illustrative purposes.MSC 2010 subject classifications: 62G05, 62G07, 62G32.

The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate extreme events is convenient for end users who need a large number of random replications of extremes as input of a given complex system to test its sensitivity. The simulation of multivariate extremes is often based on the assumption that the dependence structure, the so-called extremal dependence function, is described by a specific parametric model. We propose a simulation method for sampling bivariate extremes, under the assumption that the extremal dependence function is semiparametric. This yields a flexible tool that can be broadly applied in real-data analyses. With the aim of estimating the probability of belonging to some extreme sets, our methodology is examined via simulation and illustrated by an analysis of strong wind gusts in France.Stat 2017; 6: 184-201 6 Analysis of high wind gustsDesigning infrastructures often requires the study of strong WGs. We illustrate the utility of our methodology analysing this type of natural process. We consider the hourly WG in metres per second, hourly WS in metres per second (m/s) and hourly air pressure at sea level in millibars recorded in Parcay-Meslay city in the northwest of France, from July 2004 to July 2013 (upper panels of Figure 4). We focus on WG and WS when a positive increment for the daily range of the air pressure (IP) is observed. Note that often strong wind takes place with stormy weather, and this implies a

This work aims to analyse the role played by relevant sustainability factors towards the implementation of maintenance interventions in the manufacturing industrial sector. In this context, we focus on industrial water distribution systems, on whose effective work depends the functioning of core plants as well as general industrial facilities. In detail, we propose a Multi-Criteria Decision-Making (MCDM) application based on the use of the Analytic Network Process (ANP) as a methodological way to prioritise maintenance interventions while considering the influence of some of the most relevant sustainability factors identified in literature. The main advantage of such an approach consists in the elaboration of a flexible maintenance procedure for companies based on a well-known and reliable multi-criteria application. The novelty of our work refers to the development of a structured link between sustainability factors and maintenance management of industrial water distribution systems, something that is fundamental in manufacturing but also in other fields of application.