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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences


Authors: Roelof Helmers and Ricardas Zitikis
Journal: Proc. Amer. Math. Soc. 133 (2005), 3703-3712
MSC (2000): Primary 60F15
DOI: https://doi.org/10.1090/S0002-9939-05-08096-2
Published electronically: June 28, 2005
MathSciNet review: 2163610
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Abstract: We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized $L$-statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodic sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of view.


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Additional Information

Roelof Helmers
Affiliation: Centre for Mathematics and Computer Science (CWI), Kruislaan 413, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Email: R.Helmers@cwi.nl

Ricardas Zitikis
Affiliation: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada N6A 5B7
Email: zitikis@stats.uwo.ca

DOI: https://doi.org/10.1090/S0002-9939-05-08096-2
Received by editor(s): July 6, 2004
Published electronically: June 28, 2005
Additional Notes: The second author was partially supported by the Netherlands Organization for Scientific Research (NWO), as well as by a Discovery Research Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2005 American Mathematical Society