Estimating parameters of Pareto distribution under interval and fuzzy uncertainty

In many application areas, we encounter heavy-tail distributions - for example, such distributions are ubiquitous in financial applications. These distributions are often described by Pareto law. There exist techniques for estimating the parameters of such corresponding Pareto distributions based on the sample x₁, ..., x_n. In practice, we often only know the values x_i with interval (or, more generally, fuzzy) uncertainty. In this paper, we show how to estimate the parameters of the Pareto distribution under such uncertainty.