Probability in the Engineering and Informational Sciences

Table of Contents - July 2012 - Volume 26, Issue 03  

Research Article

LIKELIHOOD RATIO AND HAZARD RATE ORDERINGS OF THE MAXIMA IN TWO MULTIPLE-OUTLIER GEOMETRIC SAMPLES

Baojun Dua1, Peng Zhaoa2 and N. Balakrishnana3

a1 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

a2 School of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China

a3 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 E-mail: bala@mcmaster.ca

Abstract

In this paper, we study some stochastic comparisons of the maxima in two multiple-outlier geometric samples based on the likelihood ratio order, hazard rate order, and usual stochastic order. We establish a sufficient condition on parameter vectors for the likelihood ratio ordering to hold. For the special case when n = 2, it is proved that the p-larger order between the two parameter vectors is equivalent to the hazard rate order as well as usual stochastic order between the two maxima. Some numerical examples are presented for illustrating the established results.