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# Testing for Membership to the IFRA and the NBU Classes of Distributions

*Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics*, PMLR 22:1099-1107, 2012.

#### Abstract

This paper provides test procedures to determine whether the probability distribution underlying a set of non-negative valued samples belongs to the Increasing Failure Rate Average (IFRA) class or the New Better than Used (NBU) class. Membership of a distribution to one of these classes is known to have implications which are important in reliability, queuing theory, game theory and other disciplines. Our proposed test is based on the Kolmogorov-Smirnov distance between an empirical cumulative hazard function and its best approximation from the class of distributions constituting the null hypothesis. It turns out that the least favorable distribution, which produces the largest probability of Type I error of each of the tests, is the exponential distribution. This fact is used to produce an appropriate cut-off or p-value. Monte Carlo simulations are conducted to check small sample size (i.e., significance) and power of the test. Usefulness of the test is illustrated through the analysis of a set of monthly family expenditure data collected by the National Sample Survey Organization of the Government of India.