Comments on two papers concerning estimation of the parameters of the Pareto distribution in the presence of outliers

In this paper, we examine and correct various results relating to estimation of a Pareto distribution in the presence of outliers according to a model introduced by Dixit and Jabbari Nooghabi (2011) [1] and further studied by Dixit and Jabbari Nooghabi (2011) [2]. In particular, Dixit and Jabbari Nooghabi (2011) [2] state that the maximum likelihood estimators for the parameters appearing in their model do not exist. We show that these estimators can in fact exist, and we present and illustrate a method for determining them when they do. Two numerical illustrations using actual insurance data are included.