Outlier-prone and outlier-resistant distributions

Neyman and Scott [3] have considered the ideas of outlier-proneness and outlier-resistance of families of distributions. Under their definition, individual distributions (one-member families) cannot be outlier-prone. This paper offers definitions of outlier-proneness and outlier-resistance that apply to individual distributions, and theorems are given showing the connection with the classical laws of large numbers for maxima.