ISSN:
1436-3259
Keywords:
Crossing theory
;
exponential autocovariance model
;
discrete time series
;
Weibull distribution
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
,
Energy, Environment Protection, Nuclear Power Engineering
,
Geography
,
Geosciences
Notes:
Abstract An expression is derived for the probability distribution of excursion lengths above a fixed level, for the specific case of a discrete random process sampled from an underlying, continuous normal process with exponential autocovariance function. The expression can be integrated numerically for small excursion lengths, and used with time-series simulations to qualitatively reveal the form of the distribution. Such computations indicate that excursions lengths are well approximated by a Weibull distribution to at least the 0.95 probability value. The fit improves with increasing fixed level, and with decreasing time constant of the process. In addition, an expression is given for the expected number of crossings of a fixed level, analogous to well known formulae used in estimating expected values for the cases of a continuous process and a discrete stepped process.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01581448
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