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Weak convergence of the adjusted range of cumulative sums of exchangeable random variables

Published online by Cambridge University Press:  14 July 2016

Brent M. Troutman
Brent M. Troutman*
Affiliation:
U. S. Geological Survey
*
∗ Postal address: U.S. Geological Survey, Denver Federal Center, Box 25046, MS 420, Denver, CO 80225, U.S.A.
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Abstract

Let be the adjusted range of the cumulative sums of a sequence , where . Weak convergence results for random functions constructed from cumulative sums of {Xs} are used to obtain the asymptotic distribution and moments of when {Xs} are exchangeable, or symmetrically dependent, random variables.

Keywords

FUNCTIONAL CENTRAL LIMIT THEOREMEXCHANGEABLE SEQUENCES
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 297 - 304
Copyright
Copyright © Applied Probability Trust 1983 

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