Generalized fractional negative binomial process

Ritik Soni and Ashok Kumar Pathak

Statistics & Probability Letters, 2024, vol. 207, issue C

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) Lévy 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 Lévy subordinator and the GFNBP are also presented.

Keywords: Fractional negative binomial process; Mittag-Leffler Lévy process; Stable subordinators; Infinite divisibility; PDEs (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.110021

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