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Some results on normalized total time on test and spacings

Author

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  • Ebrahimi, Nader
  • Spizzichino, Fabio

Abstract

Let Y1, Y2,..., Yn be non-negative random variables and let Y1 [less-than-or-equals, slant] Y(2) [less-than-or-equals, slant] ... [less-than-or-equals, slant] Y(n) denote order statistics. In this manuscript, we study several properties of Di = (n - i + 1)(Y(i) - Y(i-1)), I = 1,2,..., n, where Y(0) [not identical with] 0. In particular we characterize the relevant case of lifetimes with Schur-constant density in terms of the joint density function of D1,..., Dn. We also analyze properties of Schur-concave (convex) densities and of the functions g(i) = E{Di} and .

Suggested Citation

  • Ebrahimi, Nader & Spizzichino, Fabio, 1997. "Some results on normalized total time on test and spacings," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 231-243, December.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:3:p:231-243
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    References listed on IDEAS

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    1. Cooke, Roger M., 1993. "The total time on test statistic and age-dependent censoring," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 307-312, November.
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    Cited by:

    1. Nappo, G. & Spizzichino, F., 1998. "Ordering properties of the TTT-plot of lifetimes with Schur joint densities," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 195-203, August.
    2. Chu, Yu-Ming & Xia, Wei-Feng & Zhang, Xiao-Hui, 2012. "The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 412-421.

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