Tests of randomness in two dimensions
A.M. Liebetrau · Communication in Statistics- Theory and Methods · 1977
In an earlier paper, the author shows that a suitably normalized estimator of the variance function of a two-dimensional Poisson process converges to a two-dimensional nonstationary Gaussian process . In this paper, distributions of the functionals and are obtained, and computing formulas for sample analogues are given. The first is a normal random variable; the characteristic function, the first two moments and an approximation to the upper tail of the distribution function of the second are given. Finally, tests of “marginal randomness” based upon are considered.