In this paper we propose several goodness-of-fit tests based on robust measures of skewness and tail weight. They can be seen as generalisations of the Jarque–Bera test (Bera and Jarque in Econ Lett 7:313–318, 1981) based on the classical
skewness and kurtosis, and as an alternative to the approach of Moors et al. (Stat Neerl 50:417–430, 1996) using quantiles. The power values and the robustness properties
of the different tests are investigated by means of simulations and applications on real data.We conclude that MC-LR, one of our proposed tests, shows the best overall
power and that it is moderately influenced by outlying values.