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Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences

Author

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  • Mansour Shrahili

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mohamed Kayid

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

In this paper, several characterizations for exponential distribution are derived from a new relative hazard rate measure. This measure is closely related to the concept of remaining lifetime at a random time. It considers the random times specified by the order statistics of a sample, the convolution of random variables, and the record values of a sequence of random variables. The concept of completeness in functional analysis provides the technical background to obtain the main results.

Suggested Citation

  • Mansour Shrahili & Mohamed Kayid, 2022. "Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3052-:d:896758
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    References listed on IDEAS

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    7. Arijit Patra & Chanchal Kundu, 2019. "On generalized orderings and ageing classes for residual life and inactivity time at random time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 691-704, August.
    8. Farbod Roosta-Khorasani & Gábor Székely, 2015. "Schur properties of convolutions of gamma random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 997-1014, November.
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    Cited by:

    1. Mohamed Kayid & Mansour Shrahili, 2023. "Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis," Mathematics, MDPI, vol. 11(6), pages 1-15, March.

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