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

In 1990, Jakeman (see \cite{jakeman1990statistics}) 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 o...

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Published in:arXiv.org 2024-05
Main Authors: Meena Sanjay Babulal, Gauttam, Sunil Kumar, Maheshwari, Aditya
Format: Article
Language:English
Subjects:
Algorithms
Markov processes
Method of moments
Parameter estimation
Online Access:Get full text
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Summary:In 1990, Jakeman (see \cite{jakeman1990statistics}) 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 \cite{cahoy2012fractional}) 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.
ISSN:2331-8422