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The skew-normal distribution and various generalizations have received much attention in recent years in behalf of their non-normal characteristics, such as heavy right or left tail, which are appeared in many real data sets. So far, many mathematical results have been derived about the skew distributions. Nevertheless, less attention has been paid on the inferential aspects of the proposed distributions. Hence in this paper, we focus on some inferential results of the skew-normal distribution. The amount of Fisher information in the order statistics of a simple random sample is studied and some properties are discussed with respect to variations of skewness parameter. Also, the most informative part of a sample is determined via simulation. The maximum likelihood estimators of skewness parameter are derived based on both complete sample and the most informative part of the sample and their efficiencies are compared. Furthermore, a ranked based sampling scheme is introduced to do inference about the skewness parameter in populations with high right skewness. Finally, a real data set is used to illustrate the results of the paper.

Inference on skew-normal distribution based on Fisher information in order statistics