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

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  • 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
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    References listed on IDEAS

    as
    1. 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.
    2. Beghin, L., 2012. "Random-time processes governed by differential equations of fractional distributed order," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1314-1327.
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