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Characterizations of identically distributed independent random variables using order statistics

Author

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  • Bapat, R. B.
  • Kochar, Subhash C.

Abstract

Suppose X1,...Xn are independent random variables of continuous type with proportional hazard (or failure) rates. Let X(r) denote the rth order statistic and let I(r) = i if Xi = X(r). It is proved that Xi's are identically distributed if and only if X(r) and I(r) are independent for some r [set membership, variant] {2,...,n}. The second characterization is in terms of order statistics from subsamples.

Suggested Citation

  • Bapat, R. B. & Kochar, Subhash C., 1993. "Characterizations of identically distributed independent random variables using order statistics," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 225-230, June.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:3:p:225-230
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    Cited by:

    1. Malov, S.V., 1996. "On characterizations of independent identically distributed random variables via order structures," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 97-104, February.

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