Analysis of Order Statistics from Distributions with Regularly Varying Tails

Abstract

In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002, 2004). Extensions to coherent systems are mentioned as well.

Keywords:

• Coherent systems
• Increasing and convex (concave) order
• Lorenz order
• Order statistics
• regular variation.

Mathematics Subject Classifications:

• 60E15
• 60K10.