Applications of Mathematics, Vol. 65, No. 3, pp. 245-255, 2020
Some consistent exponentiality tests based on Puri-Rubin and Desu characterizations
Marija Cuparić, Bojana Milošević, Yakov Yu. Nikitin, Marko Obradović
Received November 22, 2019. Published online May 21, 2020.
Abstract: We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an $L^2$-distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of the tests is assessed through local Bahadur efficiencies as well as the empirical power for small and moderate sample sizes. According to both criteria, for many common alternatives, our tests perform better than the integral and Kolmogorov-type tests based on the same characterizations.
Keywords: goodness-of-fit; asymptotic efficiency; V-statistics; characterization; test for exponentiality
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Affiliations: Marija Cuparić (corresponding author), Bojana Milošević, University of Belgrade, Faculty of Mathematics, Studenski trg 16, 11000 Belgrade, Serbia, e-mail: marijar@matf.bg.ac.rs, bojana@matf.bg.ac.rs; Yakov Yu. Nikitin, Department of Mathematics and Mechanics, Saint-Petersburg State University, Universitetskaia nab. 7/9, Saint Petersburg, 199034 Russia; National Research University - Higher School of Economics, Souza Pechatnikov, 16, Saint Petersburg, 190008 Russia, e-mail: yanikit47@mail.ru; Marko Obradović, University of Belgrade, Faculty of Mathematics, Studenski trg 16, 11000 Belgrade, Serbia, e-mail: marcone@matf.bg.ac.rs
