A Test for Convex Dominance With Respect to the Exponential Class Based on an L-1 Distance

作者：Baillo Amparo^*; Carcamo Javier; Nieto Sofia

来源：IEEE Transactions on Reliability, 2015, 64(1): 71-82.

DOI：10.1109/TR.2014.2355534

• Ageing classes of distributions
• convex order
• exponential distribution
• harmonic new better than used in expectation

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 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.

• 出版日期2015-3