It has been shown in this paper that a test proposed by Barlow and Doksum (1972) based on the exponential scores statistic for testing exponentiality against increasing failure rate distributions is consistent for the much wider class of harmonic new better than used in expectation distributions.

We establish the equivalence of conditional unbiasedness and Lehmann's risk unbiasedness and a necessary and sufficient condition for the existence of such estimators. This condition brings out transparently the reason for the nonexistence of such estimators in most cases based on single stage...

A two-sample Mood median test, along with an associated confidence interval, is developed for the contrast parameter of the treatment and control medians, under an order restricted randomization. The exact and asymptotic null distributions of the test statistic are derived. It is shown that the...