Convergence criteria for interval-valued inequality indices

Abstract

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.

Keywords:

• Hausdorff distance
• Interval-valued inequality indices
• Random intervals
• Statistical inequality indices

Acknowledgments

The authors are deeply grateful to the referees and the Associate Editor of this paper for their helpful comments and suggestions. The research in this paper has been partially supported by the Grants MCT-BFM2002-01057 and MCT-BFM2002-03263 from the Spanish Ministry of Science and Technology. This financial support is thankfully acknowledged. The research has also been supported by the Grants Ignacio Cascos received from the British Council and the Spanish Ministry of Science and Technology (FP1999-10887635) to spend some research stays under the guidance of Professor Ilya Molchanov as a postgrade visitor. The authors want to express their deepest gratitude to Professor Molchanov for his helpful discussions and support.