For a partition P of a set C we prove that if P maximizes the generalized utilitarian social welfare function then P is a Pareto optimal partition. We also give a condition under whic the partition that maximizes is unique. Mathematics Subject Classification: 58E17, 91B15

The paper deals with the estimation problem for the generalized Pareto distribution based on progressive type-II censoring with random removals. The number of components removed at each failure time is assumed to follow a binomial distribution. Maximum likelihood estimators and the asymptotic variance-covariance matrix of the estimates are obtained. Finally, a numerical example is given to illu...

We propose a very weak type of generalized distance called weak τ -function and use it to weaken the assumptions about lower semicontinuity in existing formulations of Ekeland’s variational principle for a kind of minimizers of a set-valued mapping, which is different from the Pareto minimizer, and in recent results which are equivalent to Ekeland’s variational principle.

• Using resistant and robust methods we propose the statistic Tn= (FU−M)/(M−FL) for testing exponentiality versus generalized Pareto, where FU , FL and M are, respectively, the upper and lower fourths and the median of a random sample of size n. The statistic Tn is based on the statistic Vn= (Xn:n−M)/(M−X1:n) used by Gomes (1982) to discriminate extremal models in a similar context but with a h...

This paper presents a continuous one parameter family of multivariate generalized Pareto distributions which describe the asymptotic behaviour of exceedances over linear thresholds. The one–dimensional theory has proved to be important in insurance, finance and risk management. The multivariate limit theory presented here is developed with similar applications in mind.

A widely used tool in the study of risk, insurance and extreme values is the mean excess plot. One use is for validating a Generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects of the use of the mean excess plot.

Generalized scalarizing problems, called GENS and GENSLex, for obtaining Pareto optimal solutions of multicriteria optimization problems are presented in the paper. The basic properties of these scalarizing problems are described. The existence of single-criterion problems with differentiable objective functions and constraints, which are equivalent to GENS and GENSLex scalarizing problems, are...

Generalized Pareto distributions (GPD) are widely used for modeling excesses over high thresholds (within the framework of the POT-approach to modeling extremes). The aim of the paper is to give the review of the classical techniques for estimating GPD quantiles, and to apply these methods in finance to estimate the Valueat-Risk (VaR) parameter, and discuss certain difficulties related to this ...

Abstract. In this paper we consider some four-parametric, so-called Generalized Pareto-like Frequency Distribution, which have been constructed using stochastic Birth-Death Process in order to model phenomena arising in Bioinformatics (Astola and Danielian, 2007). As examples, two ”real data” sets on the number of proteins and number of residues for analyzing such distribution are given. The co...