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All Journal Asian Journal of Science, Technology, Engineering, and Art Mikailalsys Journal of Mathematics and Statistics
Alao, Bamigbala Olateju
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Arts Computer Science & IT Engineering Mathematics Mechanical Engineering Social Sciences

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Derivation of Two Parameters Poisson Rani Distribution and Its Properties Alao, Bamigbala Olateju; Peter, Pantuvo Tsoke; Babando, Ikrimat Aliyu; Gatta, Abdulganiy Abdullahi
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 1 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i1.4385

Abstract

This study introduces the Two Parameters Poisson Rani Distribution (TPPRD). The probability distribution of TPPRD is derived by assuming that the parameters of the Poisson distribution follow the Two Parameters Rani Distribution, resulting in the formation of the TPPRD. The study derives some of its fundamental properties and demonstrates that TPPRD is a special-case distribution capable of handling overdispersed count data. Additionally, the maximum likelihood estimators are used to derive equations for estimating the parameters of the Two Parameters Poisson Rani Distribution.
Derivation of Poisson Xrama Distribution and Its Properties Alao, Bamigbala Olateju; Abdulkadir, Saidu Sauta; Akinrefon, Adesupo A.; Danjuma, Jibasen
Asian Journal of Science, Technology, Engineering, and Art Vol 3 No 3 (2025): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v3i3.5294

Abstract

This study introduces the Poisson Xrama Distribution, a model for analyzing count data that exhibits overdispersion. By combining the Poisson distribution with the Xrama distribution, this model addresses the limitations of traditional Poisson models, which assume equidispersion. The Poisson Xrama Distribution offers enhanced flexibility in handling variance inflation, making it suitable for scenarios where standard Poisson models are insufficient. Key statistical properties, including moments, variance, skewness, kurtosis and index of dispersion measures are derived. Maximum likelihood estimation is employed for parameter estimation, providing a robust framework for practical applications. This distribution is particularly useful in fields where count data often display overdispersion, such as biology and economics, offering a promising alternative to existing distribution models.
A Novel Probability Distribution: Mathematical Derivation and Validation of the Poisson Hamza Model Alao, Bamigbala Olateju; Alhaji, Magaji Umar; Bawuro, Fadimatu Mohammed; Bature, Gambo Innga
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6106

Abstract

This study introduces the Poisson Hamza Distribution (PHD), a novel probability distribution developed from the classical Poisson framework to address limitations in modeling count data. While the Poisson distribution is a standard tool for modeling rare events, its inherent assumptions, particularly equidispersion, limit its applicability in complex, real-world contexts. The PHD introduces enhanced modeling flexibility by accommodating overdispersion, thereby extending the utility of Poisson-based models. A comprehensive mathematical formulation of the PHD is presented, along with derivations of its key statistical properties, including moments, variance, standard deviation, skewness, and kurtosis. Theoretical validation is supported by empirical analysis, demonstrating the distribution’s robustness and practical relevance. These contributions offer a valuable extension to existing statistical methodologies and provide researchers and practitioners with an alternative model for analyzing overdispersed count data.
Co-Authors Abdulkadir, Saidu Sauta Akinrefon, Adesupo A. Alhaji, Magaji Umar Babando, Ikrimat Aliyu Bature, Gambo Innga Bawuro, Fadimatu Mohammed Danjuma, Jibasen Gatta, Abdulganiy Abdullahi Peter, Pantuvo Tsoke