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Test of fit for Marshall-Olkin distributions with applications. (English) Zbl 1122.62054
Summary: A. W. Marshall and J. Olkin [J. Am. Stat. Assoc. 62, 30–44 (1967; Zbl 0147.38106)] 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.

##### MSC:
 62H15 Hypothesis testing in multivariate analysis 62F40 Bootstrap, jackknife and other resampling methods 60F05 Central limit and other weak theorems 65C05 Monte Carlo methods 62G10 Nonparametric hypothesis testing
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