Mantel's space-time clustering statistic: computing higher moments and a comparison of various data transforms

Mantel proposed a statistic for assessing space-time clustering. He showed how to compute its theoretical expectation and variance and pointed out its asymptotic normality, noting that a simulation approach might be used in insufficiently asymptotic situations. Another approach to this distribution problem is presented by which graduation curves (e.g. Pearson curves) are fitted to the theoretical distribution. This requires the computation of the exact first four moments and the formulae are presented herein. In terms of computer time, this compares favourably with a simulation approach. The analysis of two sets of data confirmed that normality of the test statistic cannot be taken for granted and that a variety of inverse transformations of the time and space data and Knox's method were equally robust.