Sampling distributions of skew normal populations associated with closed skew normal distributions

The sample mean and sample variance are commonly used statistics in our study. In this paper, distributions of the sample mean and sample variance from a skew normal population are derived under closed skew normal (CSN) settings. The noncentral closed skew chi-square distribution is defined, and the distribution of quadratic forms is discussed. Our results generalize the corresponding results given under skew normal settings. Several examples are given for illustration of our results.