A Nonparametric Test Procedure for Two Distributions Equality using the Right Censored Data

In this study we consider to propose a nonparametric test procedure for two distributions equality based on the several quantile test statistics with combining them into a statistic using estimated covariance matrix for the right censored data in the two-sample problem. For this, since we do not assume any specific model between two populations or distributions, our proposed test procedure can be applied to some broad situations. Then we derive the limiting distribution for the quadratic form using the large sample approximation theory by assuming that the estimated covariance matrix is positive definite. Finally we illustrate our procedure with an example and discuss some interesting features of our test as concluding remarks.