
Accession Number : AD0723226
Title : WaveLength 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 Wavelength 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 wavelength 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