The standard root-b1 test is widely used for testing skewness. However, several studies have demonstrated that this test is not reliable for discriminating between symmetric and asymmetric distributions in the presence of excess kurtosis. The main reason for the failure of the standard root-b1...

We study the asymptotic covariance function of the sample mean and quantile and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles, if and only if the underlying distribution is...