This paper presents statistical goodness-of-fit tests on worldwide seismicity data from 1980 to 2015. The tests show that earthquake temporal occurrences do not necessarily follow the Poisson distribution as it has been commonly applied to earthquake studies. On the other hand, the Weibull distribution was found a satisfactory model in capturing the observed earthquake magnitude distributions with statistical significance, which can be applied to earthquake analyses that require earthquake magnitude distributions as input. (C) 2019 Published by Elsevier B.V.