In many application areas, we encounter heavy-taildistributions -- for example, such distributions are ubiquitousin financial applications. These distributions are oftendescribed by Pareto law. There exist techniques for estimatingthe parameters of such the corresponding Pareto distributionsbased on the sample x1, ..., xn. In practice, we oftenonly know the values xi with interval uncertainty. In thispaper, we show how to estimate the parameters of the Paretodistribution under such uncertainty and how to describe deviationand dependence for general heavy-tailed distributions.