Convergence criteria for interval-valued inequality indices

In this paper we introduce an interval-valued inequality index for random intervals based on a convex function. We show that if this function does not grow faster than x ^p , then the inequality index is continuous on the space of random intervals with finite p-th moment. A bound for the distance between the inequality indices of two random intervals is also constructed. An example is presented to motivate and illustrate the developments in this paper.