On Tests for Special Two-Sample Location Problem Based on Subsample Minimum and Median

Abstract

Shetty and Umarani(2005) considered a special type of two-sample location problem which has some potential applications, particularly in comparing the performances of two packing machines. In this paper, a new class of test statistics is proposed which is based on sub-sample minima of first sample and sub-sample median of second sample. The performance of members of the new class is evaluated in terms of Pitman asymptotic relative efficiency in comparision with Shetty and Umarani(2005). It can be concluded that the performance of the new proposed class of tests is better for medium and heavy tailed distributions such as Normal, Logistic, Laplace and Cauchy. For light tailed distributions the performance of new testis better in specific cases. It is proved that the test is consistent for one-sided alternatives