Generalized Fractional Negative Binomial Process
Probability
2023-04-21 v1
Abstract
In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and its connection to PDEs. We examine the long-range dependence (LRD) property of the GFNBP and show that it is not infinitely divisible. The space fractional and the non-homogeneous variants of the GFNBP are explored. Finally, simulated sample paths for the ML Levy subordinator and the GFNBP are also presented.
Keywords
Cite
@article{arxiv.2304.10487,
title = {Generalized Fractional Negative Binomial Process},
author = {Ritik Soni and Ashok Kumar Pathak},
journal= {arXiv preprint arXiv:2304.10487},
year = {2023}
}