| Classes of life distributions reflecting a particular ageing property play a prominent role in reliability theory. In this dissertation, various inference problems relating to some of these classes of distributions are studied.;The first topic concerns the weak convergence of a U-statistic process focussing mainly on its application to testing exponentiality versus (nonexponential) increasing failure rate average distributions. The asymptotic normality of the test statistic is established. Its asymptotic relative efficiency with respect to the tests previously proposed in the literature is shown to be higher for a wide class of alternatives. Monte Carlo powers of the test for small samples also point in the same direction. Some of the results are extended to include the case of randomly right censored data, and the efficiency loss due to censoring is studied compared to the tests for the uncensored case. Extending the ideas to the bivariate distributions, a test is proposed for testing bivariate exponentiality against the class of bivariate increasing failure rate average distributions. Large sample properties of the test statistic are studied using the theory of U-statistics and asymptotic relative efficiency.;The second topic of the dissertation is the problem of estimating the measure of deviation of F from exponentiality towards NBU alternatives, denoted by... |
