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A Journal of Theoretical and Applied Statistics
Volume 49, 2015 - Issue 2
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Original Articles

Maximal dispersion of order statistics in dependent samples

Pages 386-395 | Received 13 Jul 2013, Accepted 02 Oct 2014, Published online: 24 Nov 2014

References

  • F Samaniego. On closure of the IFR class under formation of coherent systems. IEEE Trans Reliab. 1985;TR-34:69–72. doi: 10.1109/TR.1985.5221935
  • J Navarro, FJ Samaniego, N Balakrishnan, D Bhattacharya. On the application and extension of system signatures to problems in engineering reliability. Naval Res Logist. 2008;55:313–327. doi: 10.1002/nav.20285
  • T. Rychlik Projecting statistical functionals, Lecture notes in statistics, Vol. 160, Springer, New York, 2001.
  • H Yang. On the variances of median and some other order statistics. Bull Inst Math Acad Sin. 1982;10:197–204.
  • G Lin, J Huang. Variances of sample medians. Statist Probab Lett. 1989;8:143–146. doi: 10.1016/0167-7152(89)90007-2
  • N Papadatos. Maximum variance of order statistics. Ann Inst Statist Math. 1995;47:185–193. doi: 10.1007/BF00773423
  • K Jasiński, J Navarro, T Rychlik. Bounds on variances of lifetimes of coherent and mixed systems. J Appl Probab. 2009;46:894–908. doi: 10.1239/jap/1253279857
  • S Moriguti. Extremal properties of extreme value distributions. Ann Math Statist. 1951;22:523–536. doi: 10.1214/aoms/1177729542
  • N Papadatos. A note on maximum variance of order statistics from symmetric populations. Ann Inst Statist Math. 1997;49:117–121. doi: 10.1023/A:1003166723078
  • K Jasiński, T Rychlik. Maximum variance of order statistics from symmetric populations revisited. Statistics. 2013;47:422–438. doi: 10.1080/02331888.2011.648745
  • A Čiginas, D Pumputis. A note on the upper bound to variance of the sample extreme from a finite population. Commun Statist – Theory Methods. 2014;43:1793–1799. doi: 10.1080/03610926.2012.675216
  • T Rychlik. Extreme variances of order statistics in dependent samples. Statist Probab Lett. 2008;78:1577–1582. doi: 10.1016/j.spl.2008.01.013
  • K Jasiński, T Rychlik. Bounds on dispersion of order statistics based on dependent symmetrically distributed random variables. J Statist Plan Inference. 2012;142:2421–2429. doi: 10.1016/j.jspi.2012.02.019
  • PJ Huber. Robust estimation of location parameter. Ann Math Statist. 1964;35:73–101. doi: 10.1214/aoms/1177703732
  • PJ Huber, EM Ronchetti. Robust statistics. 2nd ed. Hoboken, NJ: Wiley; 2009.
  • RJ Serfling. Approximation theorems of mathematical statistics. New York: Wiley; 1980.
  • HR Varian, ‘A Bayesian approach to real estate assessement’, Studies in Bayesian econometrics and statistics in honour of L.J. Savage, S.E. Fienberg, and A. Zellner, editors, North-Holland: Amsterdam; 1975. p. 195–208.
  • T Rychlik. Distributions and expectations of order statistics for possibly dependent random variables. J Multivariate Anal. 1994;48:31–42. doi: 10.1016/0047-259X(94)80003-E
  • AW Marshall, I Olkin. Inequalities: Theory of majorization and its applications. New York: Academic Press; 1979.
  • P Miziuła, T Rychlik. Sharp bounds for lifetime variances of reliability systems with exchangeable components. IEEE Trans Reliab. 63, to appear.

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