Tests for exponentiality against NBUE alternatives: a Monte Carlo comparison

Testing of various classes of life distributions has been addressed in the literature for more than 45 years. In this paper, we consider the problem of testing exponentiality (which essentially implies no ageing) against positive ageing which is captured by the fairly large class of new better than used in expectation (NBUE) distributions. These tests of exponentiality against NBUE alternatives are discussed and compared. The empirical size of the tests is obtained by simulations. Power comparisons for different popular alternatives are done using Monte Carlo simulations. These comparisons are made for both small and large sample sizes. The paper concludes with a discussion in which suggestions are made regarding the choices of the test when a particular alternative is suspected

Hodges-Lehmann quantile-quantile plots

In this paper the Hodges-Lehmann quantile-quantile plot technique is introduced as an alternative to the quantile-quantile plot technique. The contrast between the two techniques is illustrated by a number of examples. It is found that the Hodges-Lehmann quantile-quantile plot is much smoother than the corresponding quantile-quantile plot. In particular, when a location-scale model holds, the linearity of the former is more evident than that of the latter, especially for small and moderate samples. © 1988.University of Alberta* Research supported by an NSERC Canada grant at the University of Alberta. * * Research done while visiting the University of Alberta and supported by an NSERC Canada grant of E.-E. Aly. -