  Two new test statistics are introduced to test the null hypotheses that the
sampling distribution has an increasing hazard rate on a specified interval
[0,a]. These statistics are empirical L_1-type distances between the isotonic
estimates, which use the monotonicity constraint, and either the empirical
distribution function or the empirical cumulative hazard. They measure the
excursions of the empirical estimates with respect to the isotonic estimates,
due to local non-monotonicity. Asymptotic normality of the test statistics, if
the hazard is strictly increasing on [0,a], is established under mild
conditions. This is done by first approximating the global empirical distance
by an distance with respect to the underlying distribution function. The
resulting integral is treated as sum of increasingly many local integrals to
which a CLT can be applied. The behavior of the local integrals is determined
by a canonical process: the difference between the stochastic process x ->
W(x)+x^2 where W is standard two-sided Brownian Motion, and its greatest convex
minorant.
