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Efficiency of exponentiality tests based on a special property of exponential distribution

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Abstract

New goodness-of-fit tests for exponentiality based on a particular property of exponential law are constructed. Test statistics are functionals of U-empirical processes. The first of these statistics is of integral type, the second one is a Kolmogorov type statistic.We show that the kernels corresponding to our statistics are nondegenerate. The limiting distributions and large deviations of new statistics under the null hypothesis are described. Their local Bahadur efficiency for various parametric alternatives is calculated and is comparedwith simulated powers of new tests. Conditions of local optimality of new statistics in Bahadur sense are discussed and examples of “most favorable” alternatives are given. New tests are applied to reject the hypothesis of exponentiality for the length of reigns of Roman emperors which was intensively discussed in recent years.

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Authors and Affiliations

  1. Dept. Math. Mech., St. Petersburg State Univ., St. Petersburg, Russia

    Ya. Yu. Nikitin & K. Yu. Volkova

  2. National Research Univ. - Higher School of Economics, St. Petersburg, Russia

    Ya. Yu. Nikitin

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  1. Ya. Yu. Nikitin
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  2. K. Yu. Volkova
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Correspondence to Ya. Yu. Nikitin.

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Nikitin, Y.Y., Volkova, K.Y. Efficiency of exponentiality tests based on a special property of exponential distribution. Math. Meth. Stat. 25, 54–66 (2016). https://doi.org/10.3103/S1066530716010038

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