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On recurrence relations for order statistics

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  • David, H. A.

Abstract

The main purpose of this paper is to provide a unified approach to the treatment of linear recurrence relations for single or pairs of order statistics. Suppose such a relation has been proved in the simplest case when X1, ..., Xn are independent variates having an arbitrary absolutely continuous distribution. It is pointed out that the same relation continues to hold when the X's are exchangeable, whether continuous or not. As has recently become well known, further generalizations are possible when the X's have any joint distribution. Attention is also drawn to a useful nonlinear recurrence relation due to Boncelet (1987).

Suggested Citation

  • David, H. A., 1995. "On recurrence relations for order statistics," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 133-138, August.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:2:p:133-138
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    References listed on IDEAS

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    1. Balasubramanian, K. & Bapat, R. B., 1991. "Identities for order statistics and a theorem of Rényi," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 141-143, August.
    2. N. Balakrishnan & S. Bendre & H. Malik, 1992. "General relations and identities for order statistics from non-independent non-identical variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 177-183, March.
    3. Sathe, Y. S. & Dixit, U. J., 1990. "On a recurrence relation for order statistics," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 1-4, January.
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    Cited by:

    1. Aaron Childs, 2003. "Higher order moments of order statistics from INID exponential random variables," Statistical Papers, Springer, vol. 44(2), pages 151-167, April.

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