Scaling limits for the Lego discrepancy
arXiv:hep-ph/9904343 · doi:10.1016/S0550-3213(99)00411-3
Abstract
For the Lego discrepancy with M bins, which is equivalent with a chi^2-statistic with M bins, we present a procedure to calculate the moment generating function of the probability distribution perturbatively if M and N, the number of uniformly and randomly distributed data points, become large. Furthermore, we present a phase diagram for various limits of the probability distribution in terms of the standardized variable if M and N become infinite.
16 pages