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Unimodality of the distribution of record statistics


  • Basak, Prasanta
  • Basak, Indrani


Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n[greater-or-equal, slanted]1, we denote the order statistics of X1,X2,...,Xn by X1,n[less-than-or-equals, slant]X2,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n. Define L(1)=1, L(n+1)=min{j: j>L(n), Xj>Xj-1,j-1}, andX(n)=XL(n),L(n), n[greater-or-equal, slanted]1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.

Suggested Citation

  • Basak, Prasanta & Basak, Indrani, 2002. "Unimodality of the distribution of record statistics," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 395-398, February.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:4:p:395-398

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    Cited by:

    1. 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.
    2. Cramer, Erhard, 2004. "Logconcavity and unimodality of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 83-90, June.
    3. Alimohammadi, Mahdi & Alamatsaz, Mohammad Hossein & Cramer, Erhard, 2015. "Discrete strong unimodality of order statistics," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 176-185.
    4. 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.

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