A Goodness-of-Fit Test for Additivity

In this research, we propose a testing procedure for the goodness-of-fit test to investigate whether the assumption of the additivity between two distributions holds or not. In order to apply this test to the survival analysis, we allow the data to contain the possibly right censored observations. We construct statistics with computing the difference between two different consistent interval estimates from the partitioned the positive half real line, which has been used by Akritas (1988). Also we obtain another consistent estimate of the additivity parameter as byproduct during the construction of test statistics. Then we obtain the limiting distribution of the proposed statistics using the large sample approximation theorem with a consistently estimated covariance matrix when the additivity assumption holds with some additional conditions. Then we exemplify our proposed goodness-of-test with a numerical example and comment briefly some interesting features related to the goodness-of-fit test as concluding remarks.