Parameter estimation and long-range dependence of the fractional binomial process

2024/05/14 by Meena Sanjay Babulal, Babulal, Meena Sanjay, Sunil Kumar Gauttam +3
Engineering · #60G22 #60G55 #Advanced Control Systems Design #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2405.08332

openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1990, Jakeman (see \citejakeman1990statistics) defined the binomial process as a special case of the classical birth-death process, where the probability of birth is proportional to the difference between a fixed number and the number of individuals present. Later, a fractional generalization of the binomial process was studied by Cahoy and Polito (2012) (see \citecahoy2012fractional) and called it as fractional binomial process (FBP). In this paper, we study second-order properties of the FBP and the long-range behavior of the FBP and its noise process. We also estimate the parameters of the FBP using the method of moments procedure. Finally, we present the simulated sample paths and its algorithm for the FBP.

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