Birthday Spacings Test

The birthday spacing test is an extension of the iterated spacing test described by Marsaglia in 'A current view of random number generators, Keynote Address, Statistics and Computer Science: XVI Symposium on the Interface, Atlanta, Proceedings, Elseiver'. If m birthdays are randomly chosen from a year of n days, then sorted, the number of duplicated values with parameter l = m3 /(4n). Extensive simulation with a variety of RNG's provides values of m and n for which the limiting Poisson distribution seems satisfactory. Among these is m = 1024 birthdays for a year of length n = 224 with l = 16, the version used in diehard, and more stringent versions, n = 232, 231, 230, 224, 222, 215; m = 4096, 4096, 4096, 1024, 512, 128.