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- W11701450 abstract "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 the corresponding Pareto distributions based on the sample x1, . . . , xn. In practice, we often only know the values xi with interval uncertainty. In this paper, we show how to estimate the parameters of the Pareto distribution under such uncertainty and how to describe deviation and dependence for general heavy-tailed distributions. The results of this paper partly appeared in [2, 3]. 1 Formulation of the General Problem: Estimating Parameters of the Heavy-Tailed Distributions under Interval Uncertainty Need for heavy-tailed distributions. To estimate the risk of extreme and catastrophic events, we usually perform a statistical analysis of the existing data, and use the results of this analysis to predict the probabilities (and risk) of extreme and catastrophic events. For example, based on the observations of small earthquakes recorded in a certain area, we estimate the probability of a future potentially catastrophic earthquake; based on the observed variations in the economic characteristics, we predict the probability of catastrophic (crisis) changes, etc. In most applications of statistical methods to science and engineering, researchers use either the normal distribution or distributions related to normal – such as lognormal; see, e.g., [31, 36]. In these distributions, the probability of" @default.
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- W11701450 date "2011-01-01" @default.
- W11701450 modified "2023-09-27" @default.
- W11701450 title "Estimating Risk of Extreme and Catastrophic Events under Interval Uncertainty" @default.
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