Abstract
We introduce new consistent and scale-free goodness-of-fit tests for the exponential distribution based on the Puri-Rubin characterization. For the construction of test statistics we employ weighted L2 distance between V-empirical Laplace transforms of random variables that appear in the characterization. We derive the asymptotic behaviour under the null hypothesis as well as under fixed alternatives. We compare our tests, in terms of the Bahadur efficiency, to the likelihood ratio test, as well as some recent characterization based goodness-of-fit tests for the exponential distribution. We also compare the power of our tests to the power of some recent and classical exponentiality tests. According to both criteria, our tests are shown to be strong and outperform most of their competitors.
Keywords
- Goodness-of-fit
- exponential distribution
- Laplace transform
- Bahadur efficiency
- V-statistics with estimated parameters
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Copyright
From February 2013 articles are under a Creative Commons license: CC BY-NC-ND You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work), you may not use the work for commercial purposes and you may not alter, transform, or build upon the work.
