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Two test-statistics analogous to Pearson's chi-square test function - given in (1.6) and (1.7) - are investigated. These statistics utilize, apart from the number of sample elements lying in the respective intervals of the partition, their positions within the intervals too. It is shown that the test-statistics are asymptotically distributed - as the sample size N tends to infinity - according to the x 2distribution with parameter r, i.e. the number of intervals chosen. The limiting distribution of the test statistics under the null-hypothesis when N tends to the infinity and r =O(N α) (0<α<1), further the consistency of the tests based on these statistics is considered. Some remarks are made concerning the efficiency of the corresponding goodness of fit tests also; the authors intend to return to a more detailed treatment of the efficiency later. 相似文献
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Péter Áron Seress Gábor Sándor Krisztina Vincze Ernő Klucsik Krisztián Pál Liker András 《Urban Ecosystems》2020,23(6):1311-1319
Urban Ecosystems - Alternation of day and night is the oldest cycle on Earth, which is increasingly disturbed by the accelerating rate of urbanization and technological development. Despite the... 相似文献
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