Estimation of the Second-Order Intensities of a Bivariate Stationary Point Process

Summary We consider histogram and smoothed histogram type estimates of the auto and cross intensity functions of a bivariate stationary point process. The asymptotic distributions are found to be multiples of Poissons in the histogram case and linear combinations of Poissons in the smoothed case. These asymptotic distributions suggest the plotting of the square roots of the estimates in order to stabilize the variance and to make the distributions more nearly normal. Two examples of such plots are presented in the paper.