A Class of Omnibus Tests for the Laplace Distribution based on the Empirical Characteristic Function

Abstract In this paper a class of goodness-of-fit tests for the Laplace distribution is proposed. The tests are based on a weighted integral involving the empirical characteristic function. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman's smooth test for this distribution. The new tests are compared with other omnibus tests for the Laplace distribution.

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