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Simulation and Estimation for the Fractional Yule Process

Author

Listed:
  • Dexter O. Cahoy

    (Louisiana Tech University)

  • Federico Polito

    (Sapienza University of Rome)

Abstract

In this paper, we propose some representations of a generalized linear birth process called fractional Yule process (fYp). We also derive the probability distributions of the random birth and sojourn times. The inter-birth time distribution and the representations then yield algorithms on how to simulate sample paths of the fYp. We also attempt to estimate the model parameters in order for the fYp to be usable in practice. The estimation procedure is then tested using simulated data as well. We also illustrate some major characteristics of fYp which will be helpful for real applications.

Suggested Citation

  • Dexter O. Cahoy & Federico Polito, 2012. "Simulation and Estimation for the Fractional Yule Process," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 383-403, June.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:2:d:10.1007_s11009-010-9207-6
    DOI: 10.1007/s11009-010-9207-6
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    References listed on IDEAS

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    1. Wang, Xiao-Tian & Wen, Zhi-Xiong & Zhang, Shi-Ying, 2006. "Fractional Poisson process (II)," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 143-147.
    2. Wang, Xiao-Tian & Zhang, Shi-Ying & Fan, Shen, 2007. "Nonhomogeneous fractional Poisson processes," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 236-241.
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    Cited by:

    1. Souza, Matheus de Oliveira & Rodriguez, Pablo M., 2021. "On a fractional queueing model with catastrophes," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Mohsen Alipour & Luisa Beghin & Davood Rostamy, 2015. "Generalized Fractional Nonlinear Birth Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 525-540, September.

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