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An exponential characterization based on a type II censored sample

Author

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  • Xu, Jian-Lun
  • Yang, Grace L.

Abstract

Let Si,n = [summation operator]j=1i (n - j + 1)(X(j) - X(j-1)) be the total-time-on-test at the ith order statistic X(i), 1[less-than-or-equals, slant]i[less-than-or-equals, slant]n of a random sample of n lifetimes X1, ..., Xn. Let r be a fixed integer satisfying 2[less-than-or-equals, slant]r[less-than-or-equals, slant]n, n[greater-or-equal, slanted]3. The problem that the vector (S1,n/Sr,n,...,Sr-1,n/Sr,n) has the distribution of the order statistics of r - 1 uniform (0,1) random variables implies that X1 has an exponential distribution has been studied by Seshadri et al. (1969) for the case r = n. The first complete proof of this case is given by Dufour et al. (1984). Dufour (1982) conjectured that this characterization of exponential distribution holds not only for the complete sample but also for a Type II censored sample, i.e., for r

Suggested Citation

  • Xu, Jian-Lun & Yang, Grace L., 1997. "An exponential characterization based on a type II censored sample," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 295-298, February.
    • Handle: RePEc:eee:stapro:v:31:y:1997:i:4:p:295-298
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