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Kolmogorov-Smirnov APF Test for Inhomogeneous Poisson Processes with Shift Parameter
Department of Mathematics, Higher Teachers’ Training College, University of Maroua, Maroua, Cameroon
Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Maroua, Maroua, Cameroon
- 1 Department of Mathematics, Higher Teachers’ Training College, University of Maroua, Maroua, Cameroon
- 2 Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Maroua, Maroua, Cameroon
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Abstract
In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.
KeywordsInhomogeneous Poisson ProcessKolmogorov-Smirnov Type TestParametric Basic HypothesisAsymptotic Parameter Free TestShift Parameter
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