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Contents of PMS, Vol. 33, Fasc. 1,
pages 93 - 106
 

JOINT CLUSTER COUNTS FROM UNIFORM DISTRIBUTION

Éva Osztényiné Krauczi

Abstract: We consider a vector of numbers of clusters at different distance levels of n independent identically distributed random variables uniformly distributed on [a,b] . We prove asymptotic normality of this vector when the ends a , b are known or are estimated from the sample. Basing on these asymptotic results we propose new tests for uniformity, called cluster tests. We also present results of a simulation study showing empirical behaviour of these tests.

2000 AMS Mathematics Subject Classification: Primary: 62G10; Secondary: 62G20.

Keywords and phrases: Asymptotic normality, clusters of independent uniform random variables, number of clusters, testing for uniformity.

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