Abstract: Hollander
et al. [J. Amer. Statist. Assoc. 81 (1986),
91-95] introduced the concept of the larger
class of life distributions called new better
than used of specified age. In practice, one
might be interested in the new better than
used behaviour at an unknown but estimable age
t0.Here,
we investigate the testing of new better than
used of an unknown specified age t0
(NBU-t0)
alternatives
when t0is
estimable from the data. A class of test
statistics for testing NBU-t0
(t0is
unknown) based on U-statistic,
whose kernel depends on subsample minima is
proposed. The test proposed by Ahmed [Biometrika
85(2) (1998), 451-456] for this problem
belongs to the class of tests proposed here.
The distributional properties of the class of
test statistics are studied. It is shown that,
the proposed test is distribution-free when t0
= xpand
is estimated by X([n,
p]).The
performance of few members of the proposed
class of tests is studied in terms of Pitman
asymptotic relative efficiency. The Pitman ARE
values show that the members of the class
perform well as comparison with Ahmed [Biometrika
85(2) (1998), 451-456] test. The proposed
class of tests is shown to be consistent for
NBU-t0alternatives.
