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Bounds for means and variances of progressive type II censored order statistics

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  • Balakrishnan, N.
  • Cramer, E.
  • Kamps, U.

Abstract

By applying different methods, bounds for expected values and variances of progressive type II censored order statistics are derived. Since ordinary order statistics are contained in the model, well-known bounds for their moments are obtained as particular cases. The method of the greatest convex minorant leads to close bounds for means of progressive type II censored order statistics, which are even new in the particular set-up of ordinary order statistics. Numerical examples are shown in order to compare bounds and exact values for means w.r.t. underlying rectangular and normal distributions.

Suggested Citation

  • Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:3:p:301-315
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    References listed on IDEAS

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    1. Balakrishnan, N., 1990. "Improving the hartley-David-Gumbel bound for the mean of extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 291-294, April.
    2. Papathanasiou, V., 1990. "Some characterizations of distributions based on order statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 145-147, February.
    3. Cacoullos, T. & Papathanasiou, V., 1989. "Characterizations of distributions by variance bounds," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 351-356, April.
    4. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    5. Huang, J. S., 1997. "Sharp bounds for the expected value of order statistics," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 105-107, April.
    6. Udo Kamps, 1991. "A general recurrence relation for moments of order statistics in a class of probability distributions and characterizations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 215-225, December.
    7. Rita Aggarwala & N. Balakrishnan, 1996. "Recurrence relations for single and product moments of progressive Type-II right censored order statistics from exponential and truncated exponential distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 757-771, December.
    8. Balakrishnan, N., 1993. "A simple application of binomial--negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 301-305, November.
    9. Cacoullos, T. & Papathanasiou, V., 1985. "On upper bounds for the variance of functions of random variables," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 175-184, July.
    10. Papadatos, N. & Papathanasiou, V., 1996. "A generalization of variance bounds," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 191-194, June.
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    Cited by:

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    6. Balakrishnan, N. & Burkschat, Marco & Cramer, Erhard & Hofmann, Glenn, 2008. "Fisher information based progressive censoring plans," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 366-380, December.
    7. Manoj Kumar & Anurag Pathak & Sukriti Soni, 2019. "Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal," Annals of Data Science, Springer, vol. 6(1), pages 117-152, March.
    8. Udo Kamps & Erhard Cramer, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 271-275, August.
    9. Hashemi, Marzieh & Tavangar, Mahdi & Asadi, Majid, 2010. "Some properties of the residual lifetime of progressively Type-II right censored order statistics," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 848-859, May.
    10. Erhard Cramer & Udo Kamps & Tomasz Rychlik, 2004. "Unimodality of uniform generalized order statistics, with applications to mean bounds," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 183-192, March.
    11. N. Balakrishnan & T. Rychlik, 2006. "Evaluating expectations of L-statistics by the Steffensen inequality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(3), pages 371-384, June.
    12. Marco Burkschat & Erhard Cramer & Udo Kamps, 2003. "Dual generalized order statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 13-26.
    13. Anna Dembińska, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 262-264, August.
    14. Z. Raqab, Mohammad, 2003. "P-Norm bounds for moments of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 393-402, October.
    15. Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
    16. Tomasz Rychlik, 2010. "Evaluations of generalized order statistics from bounded populations," Statistical Papers, Springer, vol. 51(1), pages 165-177, January.
    17. M. Rezapour & M.H. Alamatsaz & N. Balakrishnan, 2013. "On properties of dependent progressively Type-II censored order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 909-917, October.
    18. Cramer, Erhard & Kamps, Udo & Rychlik, Tomasz, 2002. "On the existence of moments of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 397-404, October.
    19. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    20. Hu, Taizhong & Zhuang, Weiwei, 2005. "A note on stochastic comparisons of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 163-170, April.

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