Hüsler J, Kratz M
University of Bern, Bern, Switzerland.
University Paris VI, Paris, France.
J Res Natl Inst Stand Technol. 1994 Jul-Aug;99(4):539-542. doi: 10.6028/jres.099.051.
It is known that the number of exceedances of normal sequences is asymptotically a Poisson random variable, under certain restrictions. We analyze the rate of convergence to the Poisson limit and extend the result known in the stationary case to nonstationary normal sequences by using the Stein-Chen method. In addition, we consider the cases of exceedances of a constant level as well as of a particular nonconstant level.
已知在某些限制条件下，正态序列超出正常范围的次数渐近地是一个泊松随机变量。我们分析了收敛到泊松极限的速率，并通过使用斯坦 - 陈方法将平稳情况下已知的结果扩展到非平稳正态序列。此外，我们还考虑了超出恒定水平以及特定非恒定水平的情况。
