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Discrete strong unimodality of order statistics

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  • Alimohammadi, Mahdi
  • Alamatsaz, Mohammad Hossein
  • Cramer, Erhard

Abstract

We show that discrete logconcavity of probability mass functions implies logconcavity of their distribution and survival functions. Applications are obtained and discrete strong unimodality of order statistics (OSs) is established. Illustrative examples are provided and finally discrete logconvexity of OSs is discussed.

Suggested Citation

  • Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein & Cramer, Erhard, 2015. "Discrete strong unimodality of order statistics," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 176-185.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:176-185
    DOI: 10.1016/j.spl.2015.04.019
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    References listed on IDEAS

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    1. Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
    2. 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.
    3. 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.
    4. Basak, Prasanta & Basak, Indrani, 2002. "Unimodality of the distribution of record statistics," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 395-398, February.
    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. 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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    Cited by:

    1. Mahdi Alimohammadi & Mohammad Hossein Alamatsaz & Erhard Cramer, 2016. "Convolutions and generalization of logconcavity: Implications and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 109-123, March.
    2. Alimohammadi, Mahdi & Esna-Ashari, Maryam & Cramer, Erhard, 2021. "On dispersive and star orderings of random variables and order statistics," Statistics & Probability Letters, Elsevier, vol. 170(C).

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