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

Yannis G. Yatracos

doi:10.1214/08-AAP553

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

Probability 2009-06-15 v1

Authors: Yannis G. Yatracos

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Abstract

In a sample variance decomposition, with components functions of the sample's spacings, the largest component $\tilde{I}_n$ is used in cluster detection. It is shown for normal samples that the asymptotic distribution of $\tilde{I}_n$ is the Gumbel distribution.

Keywords

asymptotic distribution cluster-index i.i.d. normal random variables sample variance decomposition Gumbel distribution

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@article{arxiv.0906.2334,
  title  = {The asymptotic distribution of a cluster-index for i.i.d. normal random variables},
  author = {Yannis G. Yatracos},
  journal= {arXiv preprint arXiv:0906.2334},
  year   = {2009}
}

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Published in at http://dx.doi.org/10.1214/08-AAP553 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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

Abstract

Keywords

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