Abstract: There is such a kind of data as heteroscedasticity, contains multiple outliers or strong influence points and skewness in the fields of economy, biomedicine and environmental science. Based on the data, this paper is concerned with the statistical diagnosis of joint location, scale and skewness models. Firstly, the Pena distance under the normal distribution is extended to the skew-normal distribution, so this method has a more widely application. Secondly, the likelihood distance, Cook distance, Pena distance and local influence analysis are used to compare the diagnostic methods, and Pena distance is better than Cook and likelihood distance  under certain conditions. Finally, through Monte Carlo simulation experiments and a real data analysis, it indicates that the theories and proposed methods in this paper are scientific and reasonable.

Key words: Pena distance, skew-normal distribution, joint location, scale and skewness models, statistical diagnostics