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Mikailalsys Journal of Mathematics and Statistics
Published by Lembaga Yasin Alsys
ISSN : 30308399     EISSN : 3030816X     DOI : https://doi.org/10.58578/mjms
Core Subject : Education, Engineering,
Engineering Mathematics Mechanical Engineering
The journal contains scientific articles covering topics such as mathematical theory, statistical methods, the application of mathematics in various disciplines, and statistical data analysis. The primary objective of this journal is to promote a better understanding of mathematical and statistical concepts and to encourage advancements in the methods and applications of mathematics and statistics in various contexts. The journal serves as a platform for researchers, academics, and practitioners to share knowledge and the latest research findings in the fields of mathematics and statistics. MJMS publishes three editions a year in February, June, and October.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 79 Documents
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Methods and Applications of Point Estimation in Inferential Statistics: A Case Study of Energy Consumption Data at ATBU Yakubu, J.; Bishir, A.; Jibril, J.; Adamu, A.; James, K. Y.; Ibrahim, A. I.
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.v3i3.7467

Abstract

This study employs established point estimation techniques in inferential statistics—including Ordinary Least Squares (OLS), Maximum Likelihood Estimation (MLE), Ridge regression, and Lasso regression—to analyze a 30-month dataset on energy consumption, billing, and revenue collection from Abubakar Tafawa Balewa University (ATBU), Bauchi. The primary objective is to assess the accuracy and efficiency of parameter estimation methods for predicting revenue based on energy billed. Using regression-based models, the study evaluates performance across two sites: the Main Campus and the Permanent Site. Empirical findings demonstrate strong model explanatory power, with R² values of approximately 0.90 and 0.80, respectively, indicating a high degree of reliability in the predictive capacity of the models. OLS is shown to provide unbiased estimates, while regularization techniques such as Ridge and Lasso improve model robustness by addressing multicollinearity and overfitting. The results highlight the practical applicability of statistical modeling in energy revenue forecasting and offer valuable insights for institutional energy management. The study concludes by recommending the integration of regularized regression techniques for more resilient forecasting frameworks in similar energy consumption environments.
Application of a Modified Adomian Decomposition Method for Solving Linear and Nonlinear Partial Differential Equations O., Okai J.; Musa, Abubakar; N., Sanda L.; M., Nasir U.; Y., Hafsat U.; S., Gidado A.; B., Mwaput D.; T., Danjuma; T., Shaukuna T.; Abdulkarim, Muhammad; U., Mujahid A.
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.v3i3.7492

Abstract

Partial Differential Equations (PDEs) are fundamental tools for modeling dynamic behaviors in physical, chemical, and engineering systems. However, solving nonlinear PDEs poses significant challenges due to the lack of closed-form solutions and the computational limitations of classical numerical approaches. This study introduces the Modified Adomian Decomposition Method (MADM) as an effective semi-analytical technique for solving both linear and nonlinear PDEs, with applications to the Advection, Burgers’, and Sine-Gordon equations. MADM enhances the classical Adomian Decomposition Method by incorporating refined recursive structures and inverse operators, which improve the convergence rate and simplify the solution process. The results demonstrate that MADM provides highly accurate solutions, often matching known exact solutions, and exhibits faster convergence compared to existing methods. Comparative analysis with the Variational Iteration Method (VIM) and the New Iteration Method (NIM) further highlights MADM’s computational efficiency and precision. These findings establish MADM as a robust and reliable tool for addressing complex PDEs across various scientific domains.
On the Numerical Solutions of Linear and Nonlinear Differential Equations by the Modified Laplace–Adomian Polynomials Method Okai, J. O.; Martha, Iliya; Adamu, M. Y.; Mujahid, U. A.; Sanda, L. N.
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7493

Abstract

This study employs the Laplace–Adomian Polynomial Method (LAPM) to obtain approximate solutions for both linear and nonlinear ordinary differential equations. LAPM integrates the Laplace transform with Adomian polynomials to manage nonlinear terms effectively, avoiding the need for linearization or perturbation techniques. To evaluate the method’s accuracy and computational efficiency, three representative examples were solved, with the results benchmarked against corresponding exact solutions. The numerical outcomes, presented through tables and graphical comparisons, demonstrate that LAPM provides highly accurate approximations with minimal error using only a few series terms. The findings affirm that the method is not only straightforward and computationally efficient but also broadly applicable to various nonlinear problems. Given its robustness and simplicity, LAPM holds promise for extension to more complex systems, including partial differential equations and multi-dimensional models in applied sciences.
On the Closed-Form Characterisation of the Impact of Risk Misprofiling on Optimal Nigerian Insurance Pricing Models Adewale, Taiwo Abiodun; Tinuoye, Oladipo Abiodun; Adebayo, Ajala Olusegun; Oluwaseyi, Olaiya Olumide; Olalekan, Owoade Olusegun; Damilare, Olaleye Peter
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7597

Abstract

This study addresses the underexplored issue of risk mis-profiling in optimal insurance pricing models and its implications for solvency and regulatory compliance within the insurance industry. It aims to mathematically analyse the effects of classification errors on premium determination, quantify pricing deviations, and assess sensitivity to misclassification biases. Adopting a quantitative research design, the study utilises insurance data spanning 2010–2020, with computational implementation in Python 3.12.3 (2025) and calibration in Weka 3.9.6 (2022). Policyholders were categorised into low-, medium-, and high-risk groups using confusion matrices, while premiums were derived under exponential utility and deterministic-equivalent principles. Analytical techniques included cumulant generating function expansions, Taylor–Lagrange remainder approximations, and optimisation frameworks. The results indicate that even minor classification errors significantly influence premium estimates, particularly due to exponential tilting, variance underestimation, and tail sensitivity. These distortions align with theoretical expectations and highlight solvency vulnerabilities when premiums fall below actuarially fair values. The study concludes that systematic mis-profiling introduces pricing inefficiencies and potential insolvency triggers. Theoretical contributions include the extension of utility-based pricing principles to account for classification uncertainty, while practical implications call for insurers and regulators to adopt robust pricing adjustments, monitor classifier accuracy, and integrate misclassification-aware pricing mechanisms. Future research directions include extending the framework to portfolio-level analysis, applying robust stochastic optimisation, and investigating the effects of machine learning classification errors on pricing precision.
Applications of the Bayesian Methods in Clinical Trials with Large Sample Size Amani, D. J; Bishir, A.; Usman, M. A.; Amos, S.; Yelwa, A.; Nyam, Peter Weng
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7483

Abstract

Bayesian methods have gained prominence as robust alternatives to traditional frequentist approaches in the design and analysis of clinical trials, particularly those involving large sample sizes. While frequentist methods rely on fixed hypotheses and long-run probability interpretations, Bayesian frameworks incorporate prior knowledge and allow for iterative updating of evidence as data accrue. This adaptability facilitates the implementation of innovative trial structures such as adaptive designs and platform trials, while also supporting real-time decision-making. The integration of historical or external data within Bayesian analyses further enhances trial efficiency, especially in interim monitoring and interpretation of treatment effects. Despite these advantages, the broader adoption of Bayesian methods in confirmatory Phase III trials remains constrained by computational demands, challenges in the elicitation and justification of prior distributions, and varying degrees of regulatory acceptance. Nevertheless, advancements in high-performance computing, the emergence of hybrid Bayesian–frequentist methodologies, and growing regulatory engagement underscore a progressive shift toward broader implementation. This paper critically examines the evolution, methodological underpinnings, and practical applications of Bayesian approaches in large-sample clinical trials, offering a comparative assessment with frequentist methods. It also outlines key benefits, prevailing limitations, and potential trajectories for future research and regulatory alignment. These insights contribute to ongoing discourse on optimizing trial design for enhanced scientific rigor, ethical standards, and decision-making in evidence-based medicine.
Development of a Predictor-Corrector Algorithm for the Numerical Solution of the Time-Fractional Vibration Equation Iyanda, Falade Kazeem; Dikko, Dauda Alani; Adefemi, Adeyemo Kolawole; Akeem, Adepoju Ajibola; Muhammad, Muhammad Yusuf; Jemilu, Shehu
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7658

Abstract

This study employs a predictor–corrector approach to solve the time-fractional vibration equation governing the transverse deflection of a cable of length L fixed at both ends. The model incorporates the Riemann–Liouville time-fractional derivative to accurately represent memory effects and damping behavior characteristic of composite and viscoelastic materials. Spatial discretization is performed using a finite difference method, while the temporal fractional derivative is approximated through a carefully formulated predictor–corrector scheme. This technique effectively addresses the initial conditions and captures the nonlocal temporal dynamics introduced by the fractional derivative. Numerical experiments demonstrate that the proposed method is accurate, stable, and computationally efficient in simulating damped vibrations in elastic and composite cables. By offering a reliable numerical framework, the approach enables more precise analysis of vibrating systems with memory effects and material heterogeneity, thereby contributing to improved modeling and design in engineering applications involving time-dependent mechanical behavior.
Alpha Power Transformed Ishita Distribution: Properties and Applications to Medical and Engineering Data Areebah, Fatima; Ieren, Terna Godfrey; Dewu, Mustapha Muhammad; Abdullahi, Jamila
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7674

Abstract

Modeling lifetime and reliability data in medicine and engineering often requires highly flexible statistical distributions capable of capturing skewed, kurtotic, and non-monotonic hazard behaviors, for which classical models such as the exponential, gamma, and Weibull distributions are often inadequate. To address this limitation, numerous generalized families of distributions have been developed, including the Alpha Power Transformed (APT) family, which has gained attention due to its simplicity and capacity to enhance the flexibility and tail behavior of some classical distributions, and the Ishita distribution, which has proven useful for modeling lifetime data with increasing or decreasing hazard rates in medical and reliability contexts. Building on these developments, this study proposes a new extension of the Ishita model known as the Alpha Power Transformed Ishita Distribution (APTID). The study derives and investigates important properties of this distribution, including its moments, moment-generating and characteristic functions, reliability measures, and order statistics, and estimates its parameters using the maximum likelihood method. The performance of the proposed APTID is evaluated using three real-life datasets, namely the remission times of bladder cancer patients, failure times of turbocharger, and body fat percentages of Australian athletes. Model selection criteria such as AIC, BIC, CAIC, and Kolmogorov–Smirnov tests indicate that the APTID consistently outperforms the transmuted Ishita, sine-Ishita, Ishita, Akash, and Lindley distributions. These results confirm that the proposed APTID will be a robust and versatile method for modeling diverse medical and engineering lifetime data.
Properties and Application of Alpha Power Transformed Perks Distribution to Engineering Data Yakura, Bassa Shiwaye; Aniah-Betiang, Elizabeth Ishagba; Koleoso, Peter O.; Ieren, Terna Godfrey
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7721

Abstract

This study introduces the Alpha Power Transformed Perks Distribution (APTPD), obtained by applying the alpha power transformation method to the classical Perks distribution in order to enhance its flexibility and enable it to accommodate different data structures. Several analytical properties of the proposed distribution are established, including a simplified expression for its probability density function, ordinary moments, moment-generating and characteristic functions, reliability measures, and order statistics. The parameter estimation for the APTPD is conducted using the method of maximum likelihood. To demonstrate its practical relevance, the APTPD is fitted to an engineering dataset on aircraft windshield service times and compared with several existing generalizations of the Perks distribution. Based on multiple goodness-of-fit statistics and information criteria, the APTPD provides the best fit among the considered competing models. Overall, the results indicate that the proposed distribution is a useful and flexible model for analyzing positively skewed lifetime data in reliability and survival studies.
Mathematical Modelling and Optimization of Inventory Control Through Linear Programming: A Case Study of Haske Modern Bakery in Bauchi State Aliyu, Umar Mujahid; Oyewola, David Opeoluwa; Taura, Joel John; Lukunti, Salisu
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7793

Abstract

This study investigates the application of linear programming optimization, complemented by primal and dual linear programming, to improve raw material allocation and maximize profitability for the Haske Modern Bakery in Bauchi, Nigeria. A mathematical model was developed to optimize raw material usage, increase production efficiency, and enhance company returns. Linear programming was employed to identify the most profitable production strategy. Additionally, the Economic Order Quantity (EOQ) model was utilized to effectively manage inventory. EOQ calculations determined the optimal order quantities for flour, sugar, butter, milk, and yeast to be approximately 59 bags, 22 bags, 11 cartons, 12 bags, and 56 cartons, respectively. The total costs of ordering flour, sugar, butter, milk, and yeast are N19,349, N11,171, N5,586, N6,119, and N27,928, respectively. Reorder points were established with stock levels triggering reorders in 20 bags of flour, 4 bags of sugar, 2 cartons of butter, 2 bags of milk, and 30 cartons of yeast, assuming a constant lead time of seven days. The results showed that the optimal production strategy involved producing 319.8294 units of small-medium loaf (X₅) and 533.0490 units of another product (Y₃), with all other products (X₁, X₂, X₃, ..., X₁₃ and Y₁, Y₂, Y₃, ..., Y₉) being zeros units. This strategy is projected to yield a maximum profit of N15991.47. This study underscores the significance of utilizing linear programming and EOQ models to enhance operational efficiency and profitability in the bakery industry.

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