The observed total time on test and the observed excess wealth

Xiaohu Li, Moshe Shaked

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Let X be a nonnegative random variable with mean μ≤∞, 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,μ). 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.

Original languageEnglish
Pages (from-to)247-258
Number of pages12
JournalStatistics and Probability Letters
Volume68
Issue number3
DOIs
StatePublished - 1 Jul 2004

Keywords

  • HNBUE
  • IFR
  • IFRA
  • NBUE
  • Pareto distribution
  • Stochastic orders

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