Statistical evidence of a significant difference between the performance of a protected group and the majority on a preemployment exam is often critical when a court decides whether the exam has a disparate impact, that is, whether the exam has a disproportionate adverse impact on minority...

We propose a new robust Jarque-Bera (RJB) test utilizing a robust measure of variance. The RJB statistic is asymptotically [chi]22-distributed and has equal or higher power than the JB test for several common alternatives to normality.

The paper focuses on existence, in the sense of Hoffmann-Jørgensen, of the maximum likelihood estimate (MLE) of the parameter for 1-dimensional exponential families. It is established that the MLE exists in most cases.