Parameter estimation and long-range dependence of the fractional binomial process
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909201585930240 |
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| author | Babulal, Meena Sanjay Gauttam, Sunil Kumar Maheshwari, Aditya |
| author_facet | Babulal, Meena Sanjay Gauttam, Sunil Kumar Maheshwari, Aditya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameter estimation and long-range dependence of the fractional binomial process Babulal, Meena Sanjay Gauttam, Sunil Kumar Maheshwari, Aditya Statistics Theory 60G22, 60G55 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. |
| title | Parameter estimation and long-range dependence of the fractional binomial process |
| topic | Statistics Theory 60G22, 60G55 |
| url | https://arxiv.org/abs/2405.08332 |