Test of fit for Marshall–Olkin distributions with applications |
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Authors: | Simos G. Meintanis |
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Affiliation: | Department of Economics, National and Kapodistrian University of Athens 8 Pesmazoglou Street, 105 59 Athens, Greece |
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Abstract: | Marshall and Olkin [1967. A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30–44], introduced a bivariate distribution with exponential marginals, which generalizes the simple case of a bivariate random variable with independent exponential components. The distribution is popular under the name ‘Marshall–Olkin distribution’, and has been extended to the multivariate case. L2-type statistics are constructed for testing the composite null hypothesis of the Marshall–Olkin distribution with unspecified parameters. The test statistics utilize the empirical Laplace transform with consistently estimated parameters. Asymptotic properties pertaining to the null distribution of the test statistic and the consistency of the test are investigated. Theoretical results are accompanied by a simulation study, and real-data applications. |
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Keywords: | Empirical Laplace transform Bivariate exponential distribution Goodness-of-fit test Parametric bootstrap |
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