A test for convex dominance with respect to the exponential class based on an L1 distance
EntityUAM. Departamento de Matemáticas
PublisherInstitute of Electrical and Electronics Engineers Inc.
10.1109/TR.2014.2355534IEEE Transactions on Reliability 64.1 (2015): 71-82
SubjectsAgeing classes of distributions; Convex order; Exponential distribution; Harmonic new better than used in expectation; Matemáticas
Rights© 2014 IEEE
We consider the problem of testing if a non-negative random variable is dominated, in the convex order, by the exponential class. Under the null hypothesis, the variable is harmonic new better than used in expectation (HNBUE), a well-known class of ageing distributions in reliability theory. As a test statistic, we propose the L1 norm of a suitable distance between the empirical and the exponential distributions, and we completely determine its asymptotic properties. The practical performance of our proposal is illustrated with simulation studies, which show that the asymptotic test has a good behavior and power, even for small sample sizes. Finally, three real data sets are analyzed
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