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On the exact distribution and mean value function of a geometric process with exponential interarrival times

Author

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  • Aydoğdu, Halil
  • Karabulut, İhsan
  • Şen, Elif

Abstract

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power series expansion is derived for the geometric renewal function by using an integral equation and evaluated in a computational perspective. Further, an extension is provided for the power series expansion of the geometric renewal function in the case of the Weibull distribution.

Suggested Citation

  • Aydoğdu, Halil & Karabulut, İhsan & Şen, Elif, 2013. "On the exact distribution and mean value function of a geometric process with exponential interarrival times," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2577-2582.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2577-2582
    DOI: 10.1016/j.spl.2013.08.003
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    Cited by:

    1. Halil Aydoğdu & İhsan Karabulut, 2014. "Power series expansions for the distribution and mean value function of a geometric process with Weibull interarrival times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(8), pages 599-603, December.
    2. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    3. Mustafa Hilmi Pekalp & Halil Aydoğdu, 2018. "An integral equation for the second moment function of a geometric process and its numerical solution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(2), pages 176-184, March.

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