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) : Lindgren,Georg

Report Date : APR 1971

Pagination or Media Count : 39

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 r(t) 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 u/u approaches 1 as u approaches infinity. (Author)

Descriptors :   (*STATISTICAL PROCESSES, THEOREMS), (*STOCHASTIC PROCESSES, DISTRIBUTION THEORY), STATISTICAL DISTRIBUTIONS, STATISTICAL FUNCTIONS, TRANSCENDENTAL FUNCTIONS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE