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On a lack of memory property of the exponential distribution

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Summary

LetX be a positive random variable with the distributionF and letG 0 be a monotone non-decreasing function such that E{G 0(X)} exists and is positive. Then under some additional conditions onF andG 0, E{G 0(X−x)|X>x}=E{G 0(X)},x≧0 implies thatF is exponential.

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Authors
  1. R. Shimizu
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The Institute of Statistical Mathematics

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Shimizu, R. On a lack of memory property of the exponential distribution. Ann Inst Stat Math 31, 309–313 (1979). https://doi.org/10.1007/BF02480287

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  • DOI: https://doi.org/10.1007/BF02480287

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