Abstract:

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance.
This paper proposes a modification of this criterion, which allows for testing hypotheses concerning the case where the sample comes from a skewed Student's distribution with an unknown number of degrees of freedom. The paper also provides power estimates for the constructed criterion, obtained through simulation of samples of various sizes.