Based on the concept of a logarithmic mean in two arguments, Pearson's Chi-square statistic is reformulated. Generalizations of the logarithmic mean are discussed, which immediately lead to new families of goodness-of-fit statistics. Thus it is possible to bridge the gap between Pearson's...

A new family of goodness-of-fit statistics for discrete multivariate data is being introduced, which has the characteristic of linking Pearson's Chi-square statistic with the log-likelihood ratio statistic, thus leading to new compromises between these two classical test statistics. Preliminary...