Nonparametric statistical inference for the two-sample location problem

Abstract

The two-sample problem occurs in many scientific fields, with a major frequency in environmental and agricultural research. Its primary goal is either to estimate the difference between certain parameters of the two populations or to test the hypotheses about the difference. The well known nonparametric procedure is Mann-Whitney-Wilcoxon test. The aim of this thesis is to develop a new statistical inference procedure for the problem by extending the Mann-Whitney-Wilcoxon test. In particular, simulated probabilities of the new proposed V statistic for the uniform, normal and exponential distributions are considered. Efficient computation algorithms are proposed to obtain the distribution functions of the V statistic. Power studies via simulation compare the new proposed procedure with Mann-Whitney-Wilcoxon procedure. Also included is a real data set.