Quantification of the environmental structural risk with spoiling ties: Is randomization worth?

Many recent works show that copulas turn out to be useful in a variety of different ap- plications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) rounding and adjustments, and eventually they may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to introduce suitable randomization procedures: here three different jittering strategies are outlined. The target of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it will be investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering practice. Practical advices and warnings about the use of randomization techniques are hence given

Stochastically ordered aggregation operators

In aggregation theory, there exists a large number of aggregation functions that are defined in terms of rearrangements in increasing order of the arguments. Prominent examples are the Ordered Weighted Operator and the Choquet and Sugeno integrals. Following a probability approach, ordering random variables by means of stochastic orders can be also a way to define aggregations of random variables. However, stochastic orders are not total orders, thus pairs of incomparable distributions can appear. This paper is focused on the definition of aggregations of random variables that take into account the stochastic ordination of the components of the input random vectors. Three alternatives are presented, the first one by using expected values and admissible permutations, then a modification for multivariate Gaussian random vectors and a third one that involves a transformation of the initial random vectors in new ones whose components are ordered with respect to the usual stochastic order. A deep theoretical study of the properties of all the proposals is made. A practical example regarding temperature prediction is provided

A generalization of a copula-based construction of fuzzy implications

In this paper we complement and generalize some constructions of fuzzy implications based on two arbitrary copulas, obtaining new fuzzy implications. By means of (restricted) aggregation functions acting on [0, 1]S, where Sis a fixed finite or infinite set, and related S-systems of fuzzy implications and transforming functions, we introduce and discuss a rather general method for constructing fuzzy implications. Several examples illustrating our results are also included

Best-possible bounds on the set of copulas with a given value of Spearman's footrule

In this paper we find pointwise best-possible bounds on the set of copulas with a given value of the Spearman’s footrule co-efficient. We show that the lower bound is always a copula but, unlike the bounds on sets of copulas with a given value of other measures, such as Kendall’s tau, Spearman’s rho and Blonqvist’s beta, the upper bound can be a copula or a proper quasi-copula. We characterised both of these cases

Supports of quasi-copulas

It is known that for every s∈]1, 2[there is a copula whose support is a self-similar fractal set with Hausdorff —and box-counting— dimension s. In this paper we provide similar results for (proper) quasi-copulas, in both the bivariate and multivariate cases