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Characterizations based on conditional expectations

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Abstract

For given real functionsg andh, first we give necessary and sufficient conditions such that there exists a random variableX satisfying thatE(g(X)|X≥y)=h(y)r x (y),∀y ∈ C x , whereC x andT X are the support and the failure rate function ofX, respectively. These extend the results of Ruiz and Navarro (1994) and Ghitany et al. (1995). Next we investigate necessary and sufficient conditions such thath(y)=E(g(X)|X≥y), for a given functionh.

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Authors and Affiliations

  1. Department of Mathematics, Chinese Military Academy, 830, FengShan, Kaohsiung, Taiwan, R.O.C.

    Jyh-Cherng Su

  2. Department of Applied Mathematics, National Sun Yat-sen University, 804, Kaohsiung, Taiwan, R.O.C.

    Wen-Jang Huang

Authors
  1. Jyh-Cherng Su
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  2. Wen-Jang Huang
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Additional information

Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 86-2115-M-110-014 and NSC 88-2118-M-110-001

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Su, JC., Huang, WJ. Characterizations based on conditional expectations. Statistical Papers 41, 423–435 (2000). https://doi.org/10.1007/BF02925761

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  • DOI: https://doi.org/10.1007/BF02925761

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