Selection of the Best New Better than used Population Based on Subsamples

The present study considers the problem of selecting the ‘Best’ new better than used(NBU) population among the several NBU populations. The procedure to select the ‘Best’ NBU population is developed based on a measure of departure from exponentiality towards NBU, proposed by Pandit and Math(2009)for the problem of testing exponentiality against NBU alternatives in one sample setting. The selection procedure is based on large sample properties of the statistic proposed in Pandit and Math(2009).We also indicate some applications of the selection procedur

The exact null distribution of the generalized Hollander-Proschan type test for NBUE alternatives

In this note we derive the exact null distribution for the test statistic proposed by Anis and Mitra (2011) for testing exponentiality against NBUE alternatives. As a special case, we obtain the exact null distribution for the test statistic proposed by Hollander and Proschan (1975). Selected critical values for different size are tabulated for these two statistics. Some remarks concerning the benefits of using the exact distribution are made.Comment: 9 pages, 3 Table

On Two-sample Test for Detecting Differences in the IFR Property of Life Distributions

A test proposed for testing whether one distribution is more Increasing Failure Rate (IFR) than another, based on a measure of IFR is presented in this paper. The asymptotic normality of the proposed test statistic was also established. The asymptotic null variance from the data was estimated since the variance depends on the unknown distribution. The Pitman asymptotic efficacies of the proposed test statistic are computed for various alternative IFR distributions

A Note on Detecting “More IFR-ness” Property of Life Distributions

In this paper, a problem of testing whether one life distribution possesses “more IFR” property than the other is considered.A new test procedure is proposed and the distribution of the test statistic is studied. The performance of the procedure is evaluated in terms of Pitman asymptotic relative efficiency. The consistency property of the test procedure is established. It is observed that the new procedure is better than the existing procedure in the literatur

Nonparametric inference about increasing odds rate distributions

To improve nonparametric estimates of lifetime distributions, we propose using the increasing odds rate (IOR) model as an alternative to other popular, but more restrictive, ``adverse ageing'' models, such as the increasing hazard rate one. This extends the scope of applicability of some methods for statistical inference under order restrictions, since the IOR model is compatible with heavy-tailed and bathtub distributions. We study a strongly uniformly consistent estimator of the cumulative distribution function of interest under the IOR constraint. Numerical evidence shows that this estimator often outperforms the classic empirical distribution function when the underlying model does belong to the IOR family. We also study two different tests, aimed at detecting deviations from the IOR property, and we establish their consistency. The performance of these tests is also evaluated through simulations