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Some new results on unimodality of generalized order statistics and their spacings

  • Alimohammadi, Mahdi
  • Alamatsaz, Mohammad Hossein
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    Because of the importance of ordered random variables and, in general, generalized order statistics (GOSs), in many branches of Statistics, a wide interest has been shown in investigating unimodality and strong unimodality of such random variables. Assuming certain restrictions on the model parameters and distributions, some authors have shown unimodality of GOSs. In this article, we shall provide some new results on unimodality of GOSs based on the population distribution function which contain and strengthen several known findings in this regard. A counterexample is also provided for the cases where the results are not valid in general. Unimodality of arbitrary spacings of GOSs based on exponential distributions is also discussed.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 11 (November)
    Pages: 1677-1682

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1677-1682
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    1. Basak, Prasanta & Basak, Indrani, 2002. "Unimodality of the distribution of record statistics," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 395-398, February.
    2. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    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. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika, Springer, vol. 58(3), pages 293-310, December.
    5. Chen, Huaihou & Xie, Hongmei & Hu, Taizhong, 2009. "Log-concavity of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 396-399, February.
    6. Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
    7. 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, vol. 56(1), pages 183-192, March.
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