The generalized ESD test, or generalized extreme studentized deviate test, is a statistical test for outliers. It is used on univariate data which follows an approximately normal distribution, and can be used to detect one or more outliers.
It is especially useful in situations where the number of outliers is not known: in other outlier tests, like the Grubbs test and the Tietjen Moore test, the number of outliers to be found must be specified beforehand. For the ESD test, you just specify an upper bound for the number of outliers.
Barnett, V. (1994). Outliers in Statistical Data 3rd Edition. Wiley.