Abstract: In this paper, by introducing a specific linear model, several influence measures are proposed for simplex distribution models (SDM), based on Barndorff-Nielsen and Jorgensen (1991), Jorgensen (1997), and Song and Tan (2000). The equivalency of case-deletion models and mean-shift outlier models in SDM is presented. The diagnostic test for varying dispersion in SDM is investigated and the score statistics are obtained.
The proposed diagnostic measures are illustrated with examples.

Key words: Cook distance, Diagnostics, Influential observation, Simplex distribution models, Score statistics, Varying dispersion