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Characterizations of distributions via the stochastic ordering property of random linear forms

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  • Lin, Gwo Dong
  • Hu, Chin-Yuan

Abstract

We first present a characterization of the normal distribution by the stochastic ordering relationship between a monomial and a random linear form of i.i.d. random variables. This extends a recent result of Oleszkiewicz (1997, Statist. Probab. Lett. 33, 277-280). Secondly, a remarkable characterization of the exponential distribution by geometric compounding is improved. And another characterization of the exponential distribution by the stochastic ordering relationship between a monomial and a linear form with random coefficients is also given. Finally, we investigate the characterization of the Laplace distribution.

Suggested Citation

  • Lin, Gwo Dong & Hu, Chin-Yuan, 2001. "Characterizations of distributions via the stochastic ordering property of random linear forms," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 93-99, January.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:1:p:93-99
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    1. Oleszkiewicz, Krzysztof, 1997. "On certain characterization of normal distribution," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 277-280, May.
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    Cited by:

    1. Chin-Yuan Hu & Gwo Dong Lin & Jordan M. Stoyanov, 2021. "Characterization of Probability Distributions via Functional Equations of Power-Mixture Type," Mathematics, MDPI, vol. 9(3), pages 1-21, January.

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