On the consistency of two tests for exponentiality against monotone failure rate alternatives (Q1080576)

This paper shows that two tests originally proposed for testing for the exponential distribution against Weibull alternatives are consistent against a much wider class of IFR-DFR alternatives. The first test is the well-known Thoman-Bain-Antle test \(\hat c \)[\textit{D. R. Thoman}, \textit{L. J. Bain} and \textit{C. E. Antle}, Inferences on the parameters of the Weibull distribution. Technometrics 11, 445-460 (1969)], based on the MLE of the shape parameter of the Weibull distribution. The second test, \(T_ n\), has been recently proposed by \textit{G. Diana} and the author [Metron 41, No.3-4, 167-181 (1983; Zbl 0545.62020)]. It has over \(\hat c\) the advantage of not involving iterative procedures, while it behaves very nearly as powerful as \(\hat c\) against Weibull alternatives.