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Some consistent exponentiality tests based on Puri-Rubin and Desu characterizations. (English) Zbl 07217108

The authors propose a new class of Cramér-von Mises-type goodness-of-fit tests for exponentiality based on two characterisations of exponentiality due to Puri-Rubin and Desu, employing \(L^2\)-distance between the corresponding \(V\)-empirical distribution functions. Asymptotic properties of the proposed tests are derived and their local Bahadur efficiencies against four class of alternatives - Weibull, Gamma, linear failure rate and mixture of exponential distributions with negative weights, have been calculated. It is found that the new tests have much higher local Bahadur efficiencies than the Kolmogorov type tests based on the same characterisations and that the tests are comparable to the corresponding integral type statistics. It is also shown that the proposed tests are consistent against all fixed alternatives and are good candidates based on a power study against a set of common alternatives, in small sample size cases.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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