f-Majorization with Applications to Stochastic Comparison of Extreme Order Statistics

Abstract

In this paper, we use a new partial order, called f-majorization order. The new order includes as special cases the majorization, the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of this order in the context of stochastic comparison for extreme order statistics of independent samples following the Frèchet distribution and scale model. We discuss stochastic comparisons of series systems with independent heterogeneous exponentiated scale components in terms of the usual stochastic order and the hazard rate order. We also derive new result on the usual stochastic order for the largest order statistics of samples having exponentiated scale marginals and Archimedean copula structure.

Keywords

• Stochastic order
• Exponentiated scale model
• Frèchet distribution
• Majorization
• f-majorization order
• Archimedean copula