Abstract
The test for exponentiality of a dataset in terms of a specific aging property constitutes an interesting problem in reliability analysis. To this end, a wide variety of tests are proposed in the literature. In this paper, the excess-wealth function is recalled and new asymptotic properties are studied. By using the characterization of the exponential distribution based on the excess-wealth function, a new exponentiality test is proposed. Through simulation techniques, it is shown that this new test works well on small sample sizes. The exact null distribution and normality asymptotic is also obtained for the statistic proposed. This test and a new empirical graph based on the excess-wealth function are applied to extreme-value examples.
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Acknowledgments
The authors wish to thank the Editor and the two anonymous referees whose comments helped to improve a previous version of this paper. This work was partly supported by a grant of Junta de Andalucía (Spain) for research group (FQM-328).
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Appendix
Appendix
In this section, we give the \({\mathbf{R}}\) code to compute critical values of our test and the estimated power for different sample sizes and parameter values for the Weibull distribution. In order to compute the powers for any other distribution, the corresponding R command should be changed.
Code 1. Computation of Critical Values for Statistic \(\Delta (F_{n})\) by using 10,000 MC samples.
Code 2. Estimated Power of the exponentiality test based on the excess-wealth function for the Weibull distribution by using 10,000 MC samples for a significance level equal to 0.05.
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Fernández-Ponce, J.M., Rodríguez-Griñolo, M.R. Testing exponentiality against NBUE distributions with an application in environmental extremes. Stoch Environ Res Risk Assess 29, 679–692 (2015). https://doi.org/10.1007/s00477-014-0981-5
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DOI: https://doi.org/10.1007/s00477-014-0981-5