Testing whether survival function is bivariate new better than used

We present statistical procedures to test that a life distribution is bivariate exponential against the alternative that it is bivariate new better than used (BNBU).     

A class of test statistics for testing whether new is better than used

A class of test statistics Is proposed for testing that a life distribution Is exponential against that it is new better than used and not exponential, Consistency, unbiasedness and the asymptotic normality for the one class of class of test are proved. The efflication are compeled and compared with some otner statinties. The proposed test is shown to perform well against other tests.     

Testing whether the survival function is multivariate new better than used

A test is proposed to test that a life distribution is multivariate exponential (MVE) against the alternative that it is multivariate new better than used (MNBU) class of alternatives. We also show that the proposed test is consistent for the alternatives of multivariate new better than used in expectations (MNBUE).     

Stochastic ordering and a class of multivariate new better than used distributions

A new characterization for the univariate class of new better than used ‘NBU’ distributions in terms of stochastic ordering is introduced. A multivariate version of this characterization is then used to define a multivariate class of NBU distributions. Basic properties of this class are derived. Comparisons and relationships of this new class with earlier classes are developed. Two multivariate new worse than used (NWU) classes of life distributions are defined and compared and their basic properties are studied.     

A simple test for new better than used in expectation

We present a statistical procedure to test that a life distribution is exponential against the al ternative that it is continuous new better than used in expectation. The test is shown to be consistent and asymptotic relative efficiency resul ts are obtained against the competitor developed earlier by Hollander and Proschan [2], for certain families of alternatives.