Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

Pareto efficiency is a widely used property in solution concepts for cooperative and non–cooperative game–theoretic settings and, more generally, in multi–objective problems. However, finding or even approximating (when the objective functions are not convex) the Pareto curve is hard. Most of the literature focuses on computing concise representations to approximate the Pareto curve or on explo...

We study Pareto optimal matchings in the context of house allocation problems. We present an O( √ nm) algorithm, based on Gale’s Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is N...

In this paper it is argued that a Carter–Penrose diagram can be viewed as a differential space.

A multiobjective optimization problem is considered in a general formulation. It is well known that the solution of the problem is not unique and represented in the objective space by a Pareto frontier. In an engineering design it can be important to provide a discrete representation of the entire Pareto surface. Meanwhile, the obtaining of a single Pareto solution may be time-consuming. Moreov...