Slepian model based independent interval approximation for the level excursion distributions

The independent interval approximation of the excursion time distributions for Gaussian processes has been used in physics and engineering. A new but related approach matches the expected value of the clipped Slepian to the expected value of a non-stationary binary stochastic process. This approach is extended to non-zero crossings and provides a probabilistic foundation for the validity of the approximations for a large class of processes. Both the above and below distributions are approximated. While the Slepian-based method was shown to be equivalent to the classical IIA for the zero-level, this is not the case for non-zero excursions.