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Power series expansions for the distribution and mean value function of a geometric process with Weibull interarrival times

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  • Halil Aydoğdu
  • İhsan Karabulut

Abstract

The geometric process is considered when the distribution of the first interarrival time is assumed to be Weibull. Its one‐dimensional probability distribution is derived as a power series expansion of the convolution of the Weibull distributions. Further, the mean value function is expanded into a power series using an integral equation. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 599–603, 2014

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  • 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.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:8:p:599-603
    DOI: 10.1002/nav.21605
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    References listed on IDEAS

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    1. Constantine, A. G. & Robinson, N. I., 1997. "The Weibull renewal function for moderate to large arguments," Computational Statistics & Data Analysis, Elsevier, vol. 24(1), pages 9-27, March.
    2. 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.
    3. 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.
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    Cited by:

    1. 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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