  The logrank test is a well-known nonparametric test which is often used to
compare the survival distributions of two samples including right censored
observations, it is also known as the Mantel-Haenszel test. The $G^{\rho}$
family of tests, introduced by Harrington and Fleming (1982), generalizes the
logrank test by using weights assigned to observations. In this paper, we
present a monotonicity property for the $G^{\rho}$ family of tests, which was
motivated by the need to derive bounds for the test statistic in case of
imprecise data observations.
