The Annals of Applied Probability

The asymptotic distribution of a cluster-index for i.i.d. normal random variables

Yannis G. Yatracos

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In a sample variance decomposition, with components functions of the sample’s spacings, the largest component Ĩn is used in cluster detection. It is shown for normal samples that the asymptotic distribution of Ĩn is the Gumbel distribution.

Article information

Ann. Appl. Probab., Volume 19, Number 2 (2009), 585-595.

First available in Project Euclid: 7 May 2009

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems

Extreme values spacings Gumbel distribution


Yatracos, Yannis G. The asymptotic distribution of a cluster-index for i.i.d. normal random variables. Ann. Appl. Probab. 19 (2009), no. 2, 585--595. doi:10.1214/08-AAP553.

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