Testing for discontinuity or type of distribution

In this paper, we propose a simple test for the continuity of a distribution function or of the type of distribution. The main advantage of our test in comparison to others, as used in earnings-management studies, for example, is that no assumptions regarding the underlying distribution function are necessary. Nonetheless, by use of the Chebyshev inequality we are able to define the upper limit of probabilities of test values. Results of Monte Carlo simulations indicate the robustness of the test in that the hypothesis of continuity for distribution functions with jumps is rejected whilst for continuous distributions it is not rejected. We also show that the test appropriately rejects/does not reject hypotheses regarding the type of distribution that a set of data follows. The test is particularly reliable for samples of more than 5000 observations. Applications employing such tests, for example in the earnings-management literature, typically exceed this threshold.