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On the stability of characterizations of the exponential distribution

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Summary

It is shown that if the distribution of min {X 1/a1, X2/a2,…, XN/aN} is close to that ofX 1, then the distribution is close to the exponential distribution.

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References

  1. Davies, L. (1979). On an integral inequality and its applications to some characterization problems, pre-print.

  2. Shimizu, R. (1979). A characterization of the exponential distribution,Ann. Inst. Statist. Math.,31, A, 367–372.

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  3. Shimizu, R. (1980). Functional equation with an error term and the stability of some characterizations of the exponential distribution,Ann. Inst. Statist. Math.,32, A, 1–16.

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  4. Shimizu, R. and Davies, L. (1981). General characterization theorems for the Weibull and the stable distributions,Sankhyã, A,43, to appear.

  5. Shimizu, R. and Davies, L. (1981). On the stability of characterization of non-normal stable distributions,Proceedings of the International Summer School on Statistical Distributions in Scientific Work, D. Reidel.

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Authors
  1. Ryoichi Shimizu
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The Institute of Statistical Mathematics

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Shimizu, R. On the stability of characterizations of the exponential distribution. Ann Inst Stat Math 33, 339–346 (1981). https://doi.org/10.1007/BF02480945

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  • DOI: https://doi.org/10.1007/BF02480945

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