Several extensions of the family (bivariate) Eyraud-Farlie-Gumbel-Morgenstern copulas (EFGM copulas) are considered. Some them well-known from literature, others have recently been suggested (copulas based on quadratic constructions, some forms convexity, and polynomial copulas). For each these we analyze which properties EFGM preserved (or even improved) (partly) lost. Such can be structural (...

In this paper, we introduce the Morgenstern type bivariate generalized exponential distribution. This distribution is an extension of Morgenstern type bivariate exponential distribution and the marginal distributions are generalized exponential distribution. We study some properties of this bivariate distribution. Also, some distributional properties of concomitants of order statistics as well ...

Abstract A prominent example of a perturbation the bivariate product copula (which characterizes stochastic independence) is parametric family Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some them perturbing copula, while others perturb general copulas. particularly interesting case based on two function...

In the present paper Shannon’s entropy for concomitants of generalized order statistics in FGM family is obtained. Application of this result is given for order statistics, record values, k-record values, and progressive type II censored order statistics. Also, we show that the Kullback-Leibler distance among the concomitants of generalized order statistics is distributionfree.

We analyze the aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals and society with sets of possible von Neumann-Morgenstern utility functions over lotteries. We generalize the classical neutrality assumption to this setting and characterize the class of neutral social welfare function. Th...

Collisions in the LPS cryptographic hash function of Charles, Goren and Lauter have been found by Zémor and Tillich [16], but it was not clear whether computing preimages was also easy for this hash function. We present a probabilistic polynomial time algorithm solving this problem. Subsequently, we study the Morgenstern hash, an interesting variant of LPS hash, and break this function as well....