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Logconcavity and unimodality of progressively censored order statistics

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  • Cramer, Erhard
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    Abstract

    Logconcavity and unimodality properties of the distribution of progressively censored order statistics are established and applications to aging notions are presented. Some extensions to generalized order statistics are discussed.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00072-0
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 1 (June)
    Pages: 83-90

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:1:p:83-90
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    Keywords: Logconcavity Unimodality Order statistics Progressively censored order statistics Generalized order statistics IFR IFRA;

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    1. 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.
    2. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    3. Aliev, Fazil Alioglu, 2003. "A comment on 'Unimodality of the distribution of record statistics'," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 39-40, August.
    4. Basak, Prasanta & Basak, Indrani, 2002. "Unimodality of the distribution of record statistics," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 395-398, February.
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    Cited by:

    1. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    2. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein & Cramer, Erhard, 2015. "Discrete strong unimodality of order statistics," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 176-185.
    3. Chen, Huaihou & Xie, Hongmei & Hu, Taizhong, 2009. "Log-concavity of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 396-399, February.
    4. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein, 2011. "Some new results on unimodality of generalized order statistics and their spacings," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1677-1682, November.

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