Testing Problem Of Two Population Distributions With Same Distribution Based On Nonparametric Method

Two-population distribution test is an important research topic in non-parametric test,and it is also the main problem of this paper.The two-population distribution test method based on non-parametric method has been studied for a long time,but the unbalanced two-population distribution test problem is widespread.Some existing non-parametric two-population distribution test methods do not perform well when the size of two samples is unbalanced.The more unbalanced the proportion of two samples,the smaller the test efficiency.To solve this problem,this paper proposes a new method called Imbalanced Sample Distribution Test(ISDT).Based on the previous research results and the empirical distribution function of two samples,this paper deduces the test statistics.By virtue of the good properties of U statistics,the approximate distribution and rejection domain of the test statistics are explained,and the theoretical proof process is given.Aiming at the ISDT test method,this paper carries out numerical simulation and empirical analysis.The results of numerical simulation show that when both populations are univariate continuous random variables,the probability and efficiency of ISDT test for making the first kind of errors are similar to Wilcoxon rank sum test;when both populations are univariate discrete random variables,the probability and efficiency of ISDT test for making the first kind of errors are better than that of Wilcoxon rank sum test;when both samples are multivariate random variables,the probability and efficiency of ISDT test for making the first kind of errors are better than that of Wilcoxon rank sum test.In machine variables,the probability of ISDT test making the first kind of error is similar to that of Hotelling T~2 test,but it is better than Hotelling T~2 test,and its efficiency is also better than Hotelling T~2 test.For the imbalanced two-population distribution test,ISDT test is superior to the above two methods.In addition,the ISDT test method was applied to wheat heavy metal monitoring data,which showed the feasibility of the method for single variable and multi-variable two-population distribution test.The ISDT test method proposed in this paper is suitable for both single-variable and two-population distribution test,and also for multivariable and two-population distribution test.The test method is suitable for two-population distribution test with imbalanced proportion of two samples,and also for two-population distribution test with balanced proportion of two samples.The test method can be used for both unilateral test of distribution size and unilateral test of distribution size.A bilateral test used to verify the equivalence of distribution.In addition,the test method can be extended to other disciplines,which can solve practical problems well.