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Tsallis' entropy bounds for generalized order statistics

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Języki publikacji
EN
Abstrakty
EN
We present sharp bounds for expectations of generalized order statistics with random indices expressed in terms of Tsallis’ entropy. The bounds are attainable and provide new characterizations of some nontrivial distributions. No restrictions are imposed on the parameters of the generalized order statistics model.
Rocznik
Strony
253--262
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
autor
  • Institute of Mathematics, Technical University of Łódź, ul. Wólczańska 215, 93-005 Łódź, Poland
autor
  • Institute of Mathematics, Technical University of Łódź, ul. Wólczańska 215, 93-005 Łódź, Poland
Bibliografia
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  • [5] N. Balakrishnan and R. Aggarwala, Progressive Censoring, Birkhäuser, Boston 2000.
  • [6] N. Balakrishnan, E. Cramer and U. Kamps, Bounds for means and variances of progressive type II censored order statistics, Statist. Probab. Lett 54 (2001), pp. 301-315.
  • [7] E. Cramer, U. Kamps and T. Rychlik, Eualuations of expected generalized order statistics in various scale units, Appl. Math. 29 (2002), pp. 285-295.
  • [8] H. A. David and H. N. Nagaraja, Order Statistics, Wiley, New York 2003.
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  • [10] M. Fernandes, Nonpmametric entropy-based tests of independence between stochastic processes, preprint, Fundacäo Getulio Vergas, Rio de Janeiro 2000.
  • [11] A. Franz and K. H. Hoffmann, Threshold accepting as limit case for a modified Tsallis statistics, Appl. Math. Lett. 16 (2003), pp. 27-31.
  • [12] L. Gajek and U. Gather, Moment inequalities for order statistics with applications to characterization of distributions, Metrika 38 (1991), pp. 357-367.
  • [13] L. Gajek and A. Okolewski, Sharp bounds on moments of generalized order statistics, Metrika 52 (2000a), pp. 27-43.
  • [14] L. Gajek and A. Okolewski, Inequalities for generalized order statistics from some restricted family of distributions, Comm. Statist. Theory Methods 29 (2000b), pp. 2427-2438.
  • [15] Z. Grudzień and D. Szynal, On the expected values of the k-th record values and associated characterizations of distributions, Probab. Statist. Decision Theory, Vol. A, Proc. 4-th Pannonian Symp. Math. Statist., Bad Tatzmannsdorf 1983, pp. 119-127.
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  • [19] A. Jurlewicz and K. Weron, Relaxation of dynamically correlated clusters, Journal of Non-Crystalline Solids 305 (2002), pp. 112-121.
  • [20] M. Kałuszka and A. Okolewski, Sharp exponential and entropy bounds on expectations of generalized order statistics, Metrika 58 (2003), pp. 159-171.
  • [21] U. Kamps, A Concept of Generalized Order Statistics, Teubner, Stuttgart 1995.
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  • [28] T. Rychlik, Projecting Statistical Functionals, Springer, New York 2001.
  • [29] O. Sotolongo-Costa, A. H. Rodriguez and G. J. Rodgers, Tsallis entropy and the transition to scaling in fragmentation, Entropy 2 (2000), pp. 172-177.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3cfd2750-94b0-48af-af43-c279a51cd9b8
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