Research Article
A Generalized Poisson–Gamma Hybrid Model for
Heavy-Tailed Count Data
Isiak Kamaldeen Olomoda*
,
Musa Yunus Olatunji
Issue:
Volume 14, Issue 4, August 2026
Pages:
90-105
Received:
2 March 2026
Accepted:
16 March 2026
Published:
27 July 2026
Abstract: In applications including insurance claim counts, epidemiology, reliability analysis, finance, and network traffic modeling, count data with over dispersion and heavy-tailed behavior are common. Because they impose exponentially decaying tails that underestimate extreme count probabilities, classical Poisson and Poisson–Gamma (Negative Binomial) models are frequently insufficient in such situations. In this study, we propose a generalized Poisson–Gamma hybrid distribution obtained by compounding a Poisson distribution with a power–Gamma mixing law. The proposed model extends the classical Poisson–Gamma framework by introducing an additional shape parameter that governs tail thickness and induces greater dispersion. An explicit infinite-series representation of the probability mass function is derived, and fundamental distributional properties are investigated. It was shown that the Negative Binomial distribution arises as a special case, ensuring model coherence. Furthermore, the proposed model exhibits heavier-than-exponential tails, and under suitable parameter regimes, its tail probabilities display polynomial decay, placing the distribution within the class of heavy-tailed count models. Estimation and inferential aspects were discussed and applications to simulated count data and Monte Carlo simulated count data were also discussed. Heavy-tailed count data demonstrate superior performance compared to classical alternatives.
Abstract: In applications including insurance claim counts, epidemiology, reliability analysis, finance, and network traffic modeling, count data with over dispersion and heavy-tailed behavior are common. Because they impose exponentially decaying tails that underestimate extreme count probabilities, classical Poisson and Poisson–Gamma (Negative Binomial) mo...
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Research Article
Stochastic Integration with Respect to Fractional Brownian Sheets and Applications to Anisotropic SPDEs
Bou Diop*
Issue:
Volume 14, Issue 4, August 2026
Pages:
106-112
Received:
19 December 2025
Accepted:
21 January 2026
Published:
20 August 2026
Abstract: This paper develops a comprehensive framework for stochastic integration with respect to multidimensional fractional Brownian sheets, with particular emphasis on the anisotropic setting where each Hurst index exceeds one-half. We introduce a regularizationbased approach that accounts for the directional structure of the sheet and establish its equivalence to the Malliavin calculus construction. Building on this foundation, we obtain wellposedness and regularity results for a class of stochastic partial differential equations driven by such sheets. The regularization method provides an intuitive interpretation of the integral while preserving the directional heterogeneity inherent in anisotropic models. We prove that the regularized integral converges in the mean-square sense to the Skorokhod integral, establishing a duality relation that connects our constructive approach to established analytical frameworks. Our well-posedness results are obtained through a fixed-point argument in suitably chosen solution spaces, while the regularity analysis relies on anisotropic versions of the classical Kolmogorov criterion. Notably, the H¨older exponents we obtain directly reflect the directional smoothness of the driving sheet. This feature has practical implications for numerical discretization and statistical estimation. Our findings extend known one-dimensional theories to genuinely multidimensional and anisotropic regimes, offering new tools for modelling systems with long-range dependence and directional heterogeneity. Applications include fluid flows with directional turbulence, financial markets with correlated assets exhibiting different memory properties, and biological tissues with anisotropic diffusion characteristics.
Abstract: This paper develops a comprehensive framework for stochastic integration with respect to multidimensional fractional Brownian sheets, with particular emphasis on the anisotropic setting where each Hurst index exceeds one-half. We introduce a regularizationbased approach that accounts for the directional structure of the sheet and establish its equi...
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