On the sample characterization criterion for normal distributions
Conventionally, it was shown that the underlying distribution is normal if and only if the sample mean and sample variance from a random sample are independent. This paper focusses on the normal population characterization theorem by showing that, if the joint distribution of a skew normal sample follows certain multivariate skew normal distribution, the sample mean and sample variance are still independent.
sample mean sample variance independence skew normal distribution moment generating function