By Danilo Abbate, Roberta De Asmundis (auth.), Christian Borgelt, Gil González-Rodríguez, Wolfgang Trutschnig, María Asunción Lubiano, María Ángeles Gil, Przemysław Grzegorzewski, Olgierd Hryniewicz (eds.)
Over the final 40 years there was a becoming curiosity to increase likelihood concept and records and to permit for extra versatile modelling of imprecision, uncertainty, vagueness and lack of know-how. the truth that in lots of real-life occasions info uncertainty is not just found in the shape of randomness (stochastic uncertainty) but additionally within the type of imprecision/fuzziness is yet one aspect underlining the necessity for a widening of statistical instruments. such a lot such extensions originate in a "softening" of classical equipment, permitting, specifically, to paintings with vague or imprecise information, contemplating obscure or generalized possibilities and fuzzy occasions, and so on. approximately ten years in the past the belief of building a recurrent discussion board for discussing new tendencies within the before-mentioned context was once born and ended in the 1st foreign convention on gentle tools in likelihood and facts (SMPS) that used to be held in Warsaw in 2002. within the following years the convention came about in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). within the present variation the convention returns to Oviedo. This edited quantity is a suite of papers provided on the SMPS 2010 convention held in Mieres and Oviedo. It supplies a entire review of present examine into the fusion of soppy tools with chance and statistics.
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Extra resources for Combining Soft Computing and Statistical Methods in Data Analysis
However, this paper is focused on evaluating robust methods for estimating the shape parameter θ (with respect to their inﬂuence on the selected Laeken indicators) once the threshold is ﬁxed. 1 Hill Estimator The maximum likelihood estimator for the shape parameter of the Pareto distribution was introduced by  and is referred to as the Hill estimator. It is given by k θˆ = k . (7) ∑i=1 log xn−i+1 − k logxn−k 20 A. Alfons et al. Note that the Hill estimator is non-robust, therefore it is included for benchmarking purposes.
J. Statist. 30(1), 17–36 (2002) 8. : A robust prediction error criterion for Pareto modelling of upper tails. Canad. J. Statist. 34(4), 639–658 (2006) 9. EU-SILC: Common cross-sectional EU indicators based on EU-SILC; the gender pay gap. EU-SILC 131-rev/04, Eurostat, Luxembourg (2004) 10. : A simple general approach to inference about the tail of a distribution. Ann. Statist. 3(5), 1163–1174 (1975) 11. : Robust methods for the estimation of selected Laeken indicators. Master’s Thesis, Vienna University of Technology (2009) 12.
7(4), 308–313 (1965) 12. : Uncertainty and incentives for nonpoint pollution control. J. Environ. Econ. Manage. 15(1), 87–98 (1988) A Comparison of Robust Methods for Pareto Tail Modeling in the Case of Laeken Indicators Andreas Alfons, Matthias Templ, Peter Filzmoser, and Josef Holzer Abstract. The Laeken indicators are a set of indicators for measuring poverty and social cohesion in Europe. However, some of these indicators are highly inﬂuenced by outliers in the upper tail of the income distribution.