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The observed total time on test and the observed excess wealth


  • Li, Xiaohu
  • Shaked, Moshe


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.

Suggested Citation

  • Li, Xiaohu & Shaked, Moshe, 2004. "The observed total time on test and the observed excess wealth," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 247-258, July.
  • Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:247-258

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    References listed on IDEAS

    1. 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.
    2. Bartoszewicz, Jaroslaw, 1986. "Dispersive ordering and the total time on test transformation," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 285-288, October.
    3. Bartoszewicz, Jaroslaw, 1995. "Stochastic order relations and the total time on test transform," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 103-110, February.
    4. 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.
    5. Waters, Howard R., 1983. "Some mathematical aspects of reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 17-26, January.
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    Cited by:

    1. Schweizer, Nikolaus & Szech, Nora, 2015. "Revenues and welfare in auctions with information release," Discussion Papers, Research Unit: Economics of Change SP II 2015-301, Social Science Research Center Berlin (WZB).
    2. Kandil Abd El-Fattah Mohamed & Mahdy Mervat Mahdy Ramadan & Kayid Mohamed, 2010. "Median Inactivity Time Function and its Reliability Properties," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 253-268, January.
    3. repec:eee:jetheo:v:170:y:2017:i:c:p:86-111 is not listed on IDEAS
    4. Schweizer, Nikolaus & Szech, Nora, 2015. "Revenues and welfare in auctions with information release," Working Paper Series in Economics 67, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    5. Félix Belzunce & Carolina Martínez-Riquelme, 2015. "Some results for the comparison of generalized order statistics in the total time on test and excess wealth orders," Statistical Papers, Springer, vol. 56(4), pages 1175-1190, November.
    6. Szech, Nora & Schweizer, Nikolaus, 2015. "Revenues and Welfare in Auctions with Information Release," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113041, Verein für Socialpolitik / German Economic Association.
    7. Xiaohu Li & Guoxin Qiu, 2007. "Some preservation results of NBUC aging property with applications," Statistical Papers, Springer, vol. 48(4), pages 581-594, October.
    8. Nikolaus Schweizer & Nora Szech, 2015. "Revenues and Welfare in Auctions with Information Release," CESifo Working Paper Series 5501, CESifo Group Munich.


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