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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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Journal : Mikailalsys Journal of Mathematics and Statistics

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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.
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