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On the Asymptotic Joint Distribution of the Sum and Maximum of Stationary Normal Random Variables

Hwai-Chung Ho and Tailen Hsing
Journal of Applied Probability
Vol. 33, No. 1 (Mar., 1996), pp. 138-145
DOI: 10.2307/3215271
Stable URL: http://www.jstor.org/stable/3215271
Page Count: 8
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On the Asymptotic Joint Distribution of the Sum and Maximum of Stationary Normal Random Variables
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Abstract

Let X1, X2, ⋯ be stationary normal random variables with ρn=cov(X0, Xn). The asymptotic joint distribution of Σi=1 n Xi and $\bigvee_{i=1}^{n} X_{i}$ is derived under the condition ρn log n→γ ∈ [0, ∞). It is seen that the two statistics are asymptotically independent only if γ=0.

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