Testing For Equality Of Two Distribution Populations Based On Nonparametric Method

It has a wide range of applications to test the equality of two populations in practice.For example,majority distributions of the old and new drug,old and new treatment method can be fitted with normal distribution.Due to the rapid increase of today's data,the type of data is also more diversified,it makes double parameters exponential distribution in survival analysis and the application of the product life become more and more widely.Therefore,in order to make a comparison about curative effect of old and new drugs or the life time of the old and new products,the study of testing whether two normal distributions or the two double parameter exponential distributions are equal is necessary.In this paper,we mainly study the non-parametric for testing the equality of two normal distributions and two exponential distributions with two-double parameters.Firstly,the likelihood ratio test for the equality of two normal populations with one mean known is studied.A new likelihood ratio test statistic is proposed which is different from one proposed by Neyman and Pearson and its exact null distribution is derived.We compare the type I error and the power test of the new test statistic with that of Neyman and Pearson by the simulation,which shows that our proposed test statistic performs better than that of Neyman and Pearson in controlling the type I error and the power.Then,the likelihood ratio test for the equality of two normal populations with one variance known is studied.We propose a new likelihood ratio test statistic and study its statistical properties,then,the related theorems are proposed.Moreover,we conduct the simulation analysis to compare the type I error and the power test of the new test statistic with that of Neyman and Pearson.Simulation studies show that our proposed test statistic performs better than that of Neyman and Pearson in controlling the type I error and the power.Finally,we consider testing the equality of two exponential distributions by using three Overlap Coefficients.The maximum likelihood estimators of three Overlap Coefficients are proposed,their properties are studied and some theorems are presented.We conduct simulation studies and compare their mean squared errors.Finally,to illustrate its application,we apply our proposed method to a practical example.