The observed total time on test and the observed excess wealth
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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Volume (Year): 68 (2004)
Issue (Month): 3 (July)
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References listed on IDEAS
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- Bartoszewicz, Jaroslaw, 1995. "Stochastic order relations and the total time on test transform," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 103-110, February.
- Waters, Howard R., 1983. "Some mathematical aspects of reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 17-26, January.
- 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.
- 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.
- 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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