We considered the ordered components, Y , of a multivariate random variable, Y, with covariance matrix Σ11 and the vector, Z , of concomitantly or induced ordered components of a secondary random vector, Z, with covariance matrix Σ22. Assuming that Σ11, Σ22 and the covariance structure between Y and Z are permutation-symmetric, the joint covariance structure for Y and Z is obtained. The case in...

We develop multivariate extensions to two variance reduction techniques { nonlinear control variates for estimating expected values, and concomitants of order statistics for estimating a distribution (including expected values, probabilities, and percentiles). We allow the relationship between Y and the X variables to be nonlinear, and consider two cases { where the relationship is additive, an...

We consider a generalization of the bivariate Farlie-Gumbel-Morgenstern (FGM) distribution by introducing additional parameters. For the generalized FGM distribution, the admissible range of the association parameter allowing positive quadrant dependence property is shown. Distributional properties of concomitants for this generalized FGM distribution are studied. Recurrence relations between m...

Extropy, as a complementary dual of entropy, has been discussed in many works literature, where it is declared for other measures an extension extropy. In this article, we obtain the extropy generalized order statistics via its and give some examples from well-known distributions. Furthermore, study residual past such models. On hand, based on Farlie–Gumbel–Morgenstern distribution, consider co...

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate condi- tions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivari- ate dispersive ordering of GOSs from one sample and Khaledi-Kochar mu...