Some results on majorization and their applications

Majorization is a key concept in studying the Schur-convex property of a function, which is very useful in the study of stochastic orders. In this paper, some results on Schur-convexity have been developed. We have studied the conditions under which a function φ defined by φ(x)=∑i=1nuig(xi) will be Schur-convex. This fills some gap in the theory of majorization. The results so developed have been used in the case of generalized exponential and gamma distributions. During this, we have also developed some stochastic properties of order statistics. •Some useful results on majorization are developed.•This enriches the theory of majorization.•As applications, some distributions have been studied.