On the lengths of crossing exursions: the case of a discrete normal process with underlying exponential autocovariance |
| |
| Authors: | D J Furbish W C Parker |
| |
| Institution: | (1) Dept. of Geology and Geophystical Fluid Dynamics Institute, B-160, Florida State University, 32306-3026 Tallahassee, Florida, USA |
| |
| 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. |
| |
| Keywords: | Crossing theory exponential autocovariance model discrete time series Weibull distribution |
| 本文献已被 SpringerLink 等数据库收录！ |
|
