IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v9y2021i1p1-12n1.html
   My bibliography  Save this article

Generalized Bernoulli process with long-range dependence and fractional binomial distribution

Author

Listed:
  • Lee Jeonghwa

    (Department of Statistics, Truman State University, USA)

Abstract

Bernoulli process is a finite or infinite sequence of independent binary variables, Xi, i = 1, 2, · · ·, whose outcome is either 1 or 0 with probability P(Xi = 1) = p, P(Xi = 0) = 1 – p, for a fixed constant p ∈ (0, 1). We will relax the independence condition of Bernoulli variables, and develop a generalized Bernoulli process that is stationary and has auto-covariance function that obeys power law with exponent 2H – 2, H ∈ (0, 1). Generalized Bernoulli process encompasses various forms of binary sequence from an independent binary sequence to a binary sequence that has long-range dependence. Fractional binomial random variable is defined as the sum of n consecutive variables in a generalized Bernoulli process, of particular interest is when its variance is proportional to n2H, if H ∈ (1/2, 1).

Suggested Citation

  • Lee Jeonghwa, 2021. "Generalized Bernoulli process with long-range dependence and fractional binomial distribution," Dependence Modeling, De Gruyter, vol. 9(1), pages 1-12, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:1-12:n:1
    DOI: 10.1515/demo-2021-0100
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2021-0100
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2021-0100?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Beghin, L., 2012. "Random-time processes governed by differential equations of fractional distributed order," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1314-1327.
    2. Delgado, Rosario, 2007. "A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 188-201, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lee Jeonghwa, 2021. "Generalized Bernoulli process: simulation, estimation, and application," Dependence Modeling, De Gruyter, vol. 9(1), pages 141-155, January.
    2. K. K. Kataria & M. Khandakar, 2022. "Generalized Fractional Counting Process," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2784-2805, December.
    3. Hongshuai Dai, 2013. "Convergence in Law to Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 26(3), pages 676-696, September.
    4. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.
    5. Rosario Delgado, 2016. "A packet-switched network with On/Off sources and a fair bandwidth sharing policy: state space collapse and heavy-traffic," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(2), pages 461-479, June.
    6. Rosario Delgado, 2016. "A two-queue polling model with priority on one queue and heavy-tailed On/Off sources: a heavy-traffic limit," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 57-85, June.
    7. K. K. Kataria & M. Khandakar, 2021. "On the Long-Range Dependence of Mixed Fractional Poisson Process," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1607-1622, September.
    8. Lee, Jeonghwa, 2020. "Wavelet estimation in OFBM: Choosing scale parameter in different sampling methods and different parameter values," Statistics & Probability Letters, Elsevier, vol. 166(C).
    9. Gajda, Janusz & Beghin, Luisa, 2021. "Prabhakar Lévy processes," Statistics & Probability Letters, Elsevier, vol. 178(C).
    10. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    11. L. Beghin & P. Vellaisamy, 2018. "Space-Fractional Versions of the Negative Binomial and Polya-Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 463-485, June.
    12. Lee, Chihoon, 2012. "Bounds on exponential moments of hitting times for reflected processes on the positive orthant," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1120-1128.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:1-12:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.