Accession Number:

ADA129628

Title:

A Non-Clustering Property of Stationary Sequences,

Descriptive Note:

Corporate Author:

FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s):

Report Date:

1983-05-01

Pagination or Media Count:

20.0

Abstract:

For a random sequence of events, with indicator variables Xi, the behavior of the expectation EX sub k ... K sub k m-1X sub 1 ...X sub n for 1 or k or k m - 1 or n can be taken as a measure of clustering of the events. When the measure on the Xs is i.i.d., or even exchangeable, a symmetry argument shows that the expectation can be no more than mn. When the Xs are constrained only to a stationary sequence, the bound deteriorates, and depends on k as well. When mn is small, the bound is roughly 2mn for k near n2 and is like mn log n for k near l or n. The proof given is partly constructive, so these bounds are nearly achieved, even though there is room for improvement for other values of k. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE