AN EMPIRICAL ANALYSIS OF THE DISTRIBUTION OF THE DURATION OF OVERSHOOTS IN A STATIONARY GAUSSIAN STOCHASTIC PROCESS

摘要

This is an empirical analysis of the distribution of the durations of overshoots in a stationary gaussian stochastic process. The problem arose as a result of the National Aeronautics and Space Administration's need for a distribution formula for the duration time that certain atmospheric variables such as wind speed or ambient temperature, exceed a specified level during a time interval of arbitrary length.nThis analysis utilizes computer simulation and statistical estimation. Realiza¬tions of stationry gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrela¬tion parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters could be estimated. Thus, given the autocorrelation parameter, crossing level mean and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time could be calculated.