JOINT CLUSTER COUNTS FROM UNIFORM DISTRIBUTION
Abstract: We consider a vector of numbers of clusters at different distance levels of
independent identically distributed random variables uniformly distributed on . We
prove asymptotic normality of this vector when the ends , 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.