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Title of Journal: Comput Stat

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Abbravation: Computational Statistics

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Springer Berlin Heidelberg

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10.1002/aoc.1347

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1613-9658

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Multivariate elliptically contoured stable distrib

Authors: John P Nolan
Publish Date: 2013/01/30
Volume: 28, Issue: 5, Pages: 2067-2089
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Abstract

Stable distributions with elliptical contours are a class of distributions that are useful for modeling heavy tailed multivariate data This paper describes the theory of such distributions presents formulas for calculating their densities and methods for fitting the data and assessing the fit Efficient numerical routines are implemented and evaluated in simulations Applications to data sets of a financial portfolio with 30 assets and to a bivariate radar clutter data set are presentedThis work is based on a presentation at a Deutsche Bundesbank Conference at Eltville Germany on 10–12 November 2005 The author would like to thank Robin Lumsdaine Robert Jernigan and Alan Isaac for discussions on computational questions The projections methods described above are now part of the STABLE program Robust Analysis Inc 2010We will not pursue it here but there are several ways of estimating gamma 0 and alpha from amplitude data a maximum likelihood estimation using f Rr b fractional moment methods using 24 and c using the first and second sample moments of log R and Lemma 1

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