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An axiomatic approach is used to develop a one-parameter family of measures of divergence between distributions. These measures can be used to perform goodness-of-fit tests with good statistical properties. Asymptotic theory shows that the test statistics have well-defined limiting distributions which are however analytically intractable. A parametric bootstrap procedure is proposed for implementation of the tests. The procedure is shown to work very well in a set of simulation experiments, anddoi:10.1080/07350015.2014.922470 fatcat:mdb33awswngppc6radm3juihyu