A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X + Y is symmetric about 0. In cases where the distribution of X is symmetric about its mean, it is easy to see that the constant random variable Y = −EX is a minimum-variance independent symmetrizer. Taking Y to have the same distribution as −X clearly...

We consider a game Gn played by two players. There are n independent random variables Z1; : : : ; Zn, each of which is uniformly distributed on [0; 1]. Both players know n, the independence and the distribution of these random variables, but only player 1 knows the vector of realizations z := (z1; : : : ; zn) of them. Player 1 begins by choosing an order zk1 ; : : : ; zknof the realizations. Pl...

Many quantitative problems in science, engineering, and economics are nowadays solved via statistical sampling on a computer. Such Monte Carlo methods can be used in three different ways: (1) to generate random objects and processes in order to observe their behavior, (2) to estimate numerical quantities by repeated sampling, and (3) to solve complicated optimization problems through randomized...

there are several theorical results about order statistics and copulas in the literature that have  been mentioned also by nelsen cite{p20}. the present study after reviewing some of these results, relies on  simulation technique to investigate the mentioned results about order statistics and copulas. the study concentrates on two well known archimedean gumbel and frank families in the case tha...

8 This work deals with the simulation of fuzzy random variables, which can be used 9 to model various realistic situations, where uncertainty is not only present in form 10 of randomness but also in form of imprecision, described by means of fuzzy sets. 11 Utilizing the common arithmetics in the space of all fuzzy sets only induces a conical 12 structure. As a consequence, it is difficult to di...

It is often the case in engineering analysis that the outcome of a (random) experiment is a numerical value: a displacement or a velocity; a Young’s modulus or thermal conductivity; or perhaps the yield of a manufacturing process. In such cases we denote our experiment a random variable. In this nutshell we develop the theory of random variables from definition and characterization to simulatio...