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Log-concavity of generalized order statistics

  • Chen, Huaihou
  • Xie, Hongmei
  • Hu, Taizhong
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    Generalized order statistics have been introduced as a unification of several models of random variables arranged in ascending order of magnitude with different interpretations and statistical applications. The purpose of this note is to investigate conditions on the underlying distribution function and on the parameters under which the generalized order statistics and their spacings have log-concave joint densities, respectively. Several well-known results in the literature are complemented and strengthened.

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

    Volume (Year): 79 (2009)
    Issue (Month): 3 (February)
    Pages: 396-399

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    Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:396-399
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    1. Mark Bagnoli & Ted Bergstrom, 2005. "Log-concave probability and its applications," Economic Theory, Springer, vol. 26(2), pages 445-469, 08.
    2. Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
    3. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 211-259, August.
    4. Balakrishnan, N. & Papadatos, N., 2002. "The use of spacings in the estimation of a scale parameter," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 193-204, April.
    5. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 290-296, August.
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