U-statistics Based Tests for Marginal Hazard Rate Orderings of Two Dependent Variables

We aim to compare marginal distributions of a bivariate random vector ( X , Y ) with reference to their hazard rates, ( h F ( t ) , h G ( t ) ) . In many applications, it is likely that the marginal hazard rates are ordered, e.g., h F ( t ) ≤ h G ( t ) . We consider two U -statistics based tests for testing equality of the marginal hazards against the alternative that they are ordered. Further, we compare these tests with the existing W and S tests when X and Y are assumed to be independent. The two proposed statistics are also extended to cover situations when the pair ( X , Y ) is subjected to independent univariate censoring. We provide extensive simulation studies based on copulae where the power performance of these tests is assessed. The marginal distributions considered are Weibull, linear failure rate, Gompertz and three other families of distributions based on copulae. We apply the tests to two real data examples.