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The Pearson's chi-square and the log likelihood ratio chi-square statistics are fundamental tools in goodnessof-fit testing. Cressie and Read (1984) constructed a general family of divergences which includes both statistics as special cases. This family is indexed by a single parameter, and divergences at either end of the scale are more powerful against alternatives of one type while being rather poor against the opposite type. Here we present several new goodness-of-fit testing proceduresdoi:10.1111/1467-9884.00325 fatcat:y6zvakhgmje4vdi7ejbnkqyqkm