exponential distribution;  Maximum likelihood estimation;  sample crash point;  Asymptotic normality

How to quantify the insensitivity of a statistical method to outliers has always been an important topic in robust statistical research. The sample collapse point of the test is the minimum proportion of outliers in the sample that can reverse the verdict. On the basis of studying relevant literature, the sample collapse point of the exponential distribution parameter maximum likelihood estimation test is calculated, and the asymptotic normality of the sample collapse point is analyzed, which provides a new way for the robustness of quantitative statistical methods.