The asymptotic distribution of a cluster-index for i.i.d. normal random variables - Yatracos, Yannis G. (My University, 2009)
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.
Keywords: Extreme values; Gumbel distribution; Spacings