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The observed total time on test and the observed excess wealth

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  • Li, Xiaohu
  • Shaked, Moshe
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    Abstract

    Let X be a nonnegative random variable with mean [mu][less-than-or-equals, slant][infinity], and let TX be the total time on test transform of X. It has been observed in the literature that the inverse of TX is a distribution function with support (0,[mu]). In this paper, we identify the random variable that has this distribution, and we study some of its properties. We also study an analogous random variable that is based on what is called the excess wealth transform.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 3 (July)
    Pages: 247-258

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:247-258

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    Related research

    Keywords: Stochastic orders Pareto distribution NBUE IFR IFRA HNBUE;

    References

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    1. Bartoszewicz, Jaroslaw, 1998. "Applications of a general composition theorem to the star order of distributions," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 1-9, May.
    2. Waters, Howard R., 1983. "Some mathematical aspects of reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 17-26, January.
    3. Bartoszewicz, Jaroslaw, 1986. "Dispersive ordering and the total time on test transformation," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 285-288, October.
    4. Belzunce, F., 1999. "On a characterization of right spread order by the increasing convex order," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 103-110, November.
    5. Bartoszewicz, Jaroslaw, 1995. "Stochastic order relations and the total time on test transform," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 103-110, February.
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    Cited by:
    1. Xiaohu Li & Guoxin Qiu, 2007. "Some preservation results of NBUC aging property with applications," Statistical Papers, Springer, vol. 48(4), pages 581-594, October.

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