Summary: This paper mainly studies the double generalized linear model, considers the parameters estimation and statistical diagnosis based on the data deletion model, and compares the changes between the corresponding diagnostic statistic of the deleted model and the non-deleted model. For the first time, the Pena distance based on the double generalized linear model is proposed. Through some Monte Carlo simulation studies and a real data analysis, the differences in different diagnosis statistics for discriminating between abnormal or strong influence points were compared. The results show that the proposed theories and methods in this paper are effective.