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All Journal Mikailalsys Journal of Mathematics and Statistics
Bature, Gambo Innga
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Engineering Mathematics Mechanical Engineering

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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.
Risk Factors Associated with Mother-to-Child HIV Transmission in Wukari Local Government Areas (LGAs), Taraba State 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.v3i3.6704

Abstract

Mother-to-child transmission (MTCT) of HIV continues to pose a major public health concern in Nigeria, particularly in sub-Saharan Africa. This study investigated the factors influencing MTCT of HIV in Wukari Local Government, Taraba State, using secondary data from 550 nursing mothers attending the General Hospital. A cross-sectional design was adopted, with chi-square tests used to assess associations between MTCT and maternal characteristics, while binary logistic regression identified predictors of transmission. The MTCT rate was 11.5% (63/550). Chi-square analysis revealed significant associations with maternal age (χ² = 8.181, p = 0.017), mode of delivery (χ² = 68.469, p < 0.001), maternal education (χ² = 12.729, p = 0.005), and antenatal care (ANC) visits (χ² = 36.672, p < 0.001). Logistic regression showed that mothers aged 25–35 years (OR = 3.299) and above 35 years (OR = 3.930) had higher odds of transmission than those under 25. Caesarean delivery markedly increased transmission risk (OR = 15.964), while ANC visits were unexpectedly associated with higher odds (OR = 12.851). Higher maternal weight appeared protective (OR = 0.951). The findings demonstrate that maternal age, delivery mode, and ANC patterns are significant determinants of MTCT of HIV. Targeted interventions are needed for older mothers and to strengthen prevention strategies, particularly in the context of caesarean deliveries, to reduce transmission rates and improve maternal–child health outcomes.
Co-Authors Alao, Bamigbala Olateju Alhaji, Magaji Umar Bawuro, Fadimatu Mohammed