Accession Number:

AD0723226

Title:

Wave-Length and Amplitude for a Stationary Process after a High Maximum: Decreasing Covariance Function.

Descriptive Note:

Research rept.,

Corporate Author:

NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1971-04-01

Pagination or Media Count:

39.0

Abstract:

The paper is a direct continuation of the paper Wave-length and amplitude for a stationary process after a high maximum, this series No. 742. It deals with the limiting properties as u approaches infinity of wave-length tau sub u and amplitude delta sub u after a local maximum with height u in a stationary normal process. It is assumed that the covariance function rt is strictly decreasing for t 0. The limiting distribution of tau sub u is derived and expressed by means of a certain time transformation and it includes a slight generalization of the Poisson limit theorem for crossings of a very high level. Especially it is shown that tau sub u approaches infinity and that delta sub uu approaches 1 as u approaches infinity. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE