We consider a new approach towards stochastic dominance rules. It allows measuring the degree of domination or violation of a given stochastic order and represents a way of describing stochastic orders in general. Examples are provided for the n-th order stochastic dominance and stochastic orders based on a popular risk measure.

In this paper, we introduce a new kind of order, Cesaro supermodular order, which includes supermodular order and stochastic order. For this new order, we show that it almost fulfils all desirable properties of a multivariate positive dependence order that have been proposed by Joe (1997). Also, we obtain some relations between it with other orders. Finally, we consider different issues related...

Stochastic orders and inequalities are very useful tools in various areas of economics and finance. The purpose of this paper is to describe main results obtained so far by using the idea of stochastic orders in financial optimization. Especially, the emphasis is placed on the demand and shift effect problems in portfolio selection. Some other examples, which are not related directly to optimiz...

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of functionals, aside from their large sample properties. We study a in terms usual order. For this purpose, we introduce generalized family orders, which referred transform showing that provides flexible framework for deriving monotonicity results. Given our gene...