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The observed total time on test and the observed excess wealth

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  • Li, Xiaohu
  • Shaked, Moshe

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.

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

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    1. Bartoszewicz, Jaroslaw, 1986. "Dispersive ordering and the total time on test transformation," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 285-288, October.
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    3. 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.
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    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.
    6. 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. Kandil Abd El-Fattah Mohamed & Kayid Mohamed & Mahdy Mervat Mahdy Ramadan, 2010. "Median Inactivity Time Function and its Reliability Properties," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 253-268, January.
    2. Schweizer, Nikolaus & Szech, Nora, 2017. "Revenues and welfare in auctions with information release," Journal of Economic Theory, Elsevier, vol. 170(C), pages 86-111.
    3. 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.
    4. Félix Belzunce & Carolina Martínez-Riquelme & José Ruiz, 2014. "A characterization and sufficient conditions for the total time on test transform order," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 72-85, March.
    5. 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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