Some Tests of Randomness Based Upon the Variance-Time Curve of the Poisson Process
基于泊松过程方差—时间曲线的随机性检验
Summary In an earlier paper, the author shows that a suitably normalized estimator η^0 of the variance-time curve of a Poisson process is asymptotically normal as the time of observation of the process increases. In this paper, the distributions of the functionals ζ^1c=∫01η^c(t) and ζ^2c=∫01[η^c(t)]2 are obtained, and computing formulae for the sample analogues are provided. The first is normally distributed. For the second, which is reminiscent of the Cramer-von Mises…