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An integral equation for the second moment function of a geometric process and its numerical solution

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  • Mustafa Hilmi Pekalp
  • Halil Aydoğdu

Abstract

In this article, an integral equation satisfied by the second moment function M2(t) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric function M(t) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M2(t), when the first interarrival time has an exponential distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:2:p:176-184
    DOI: 10.1002/nav.21791
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    References listed on IDEAS

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    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. W. John Braun & Wei Li & Yiqiang Q. Zhao, 2005. "Properties of the geometric and related processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 607-616, October.
    3. 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.
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