Unilag Journal of Mathematics and Applications

A BAYESIAN HERMITE REGRESSION MODEL WITH CLASSES OF PRIOR DISTRIBUTIONS APPLIED TO RIDE-HAILING PLATFORM USAGE

2026-04-16T15:35:40+00:00

Econometric and applied statistical modelling frequently encounter nonlinear datasets characterised by heavy tails, skewness, and volatility clustering. Classical regression methods, including ordinary least squares, often perform poorly under such conditions, while conventional polynomial regression may be unstable in the presence of extreme observations. To address these limitations, this study develops a Bayesian Hermite Regression Model (BHRM) that integrates truncated Hermite polynomial expansions within a coherent Bayesian framework. The model enables flexible nonlinear approximation while incorporating structured regularisation through alternative classes of prior distributions. Four prior categories—conjugate, noninformative, shrinkage, and heavy-tailed, are systematically examined to assess their influence on posterior inference and predictive behaviour. Posterior estimation is conducted using Markov Chain Monte Carlo methods, and model adequacy is evaluated using predictive and information-theoretic criteria. The results demonstrate that prior specification materially affects regularisation strength, predictive stability, and robustness to extreme demand fluctuations. Shrinkage and heavy-tailed priors enhance generalisation performance relative to standard specifications. These findings establish Bayesian Hermite regression as a scalable and principled framework for modelling nonlinear and volatile datasets such as ride-hailing demand.

A NEW APPROACH FOR MODELLING SKEWED-SEASONAL TIME SERIES DATASETS

2026-04-16T15:35:40+00:00

New models applicable to skewed distributions have been developed since the transformation changes the structure of the original series. These models fail when applied to datasets that exhibit seasonality and skewness, as accurately modeling the data structure aids in forecasting and planning. The study proposed the Skewed-Seasonal Model (SSM) for the simulated data. The results showed that the proposed Skewed-Seasonal Model (SSM) accounted for the variability in the series better than the AR model. The Skewed-Seasonal Model (SSM) approach exhibited better goodness of fit, in addition to higher forecasting ability than the AR model. The forecast evaluation metrics indicated that the forecast evaluation of the Skewed-Seasonal Model (SSM) had lower values, making the proposed Skewed-Seasonal Model (SSM) more effective than the standard Autoregressive model in capturing and predicting the behavior of skewed-seasonal time series.

BOUNDARY BEHAVIOR OF UNIVALENT HARMONIC MAPPINGS ONTO BOUNDED CONVEX DOMAINS

2026-04-16T15:35:40+00:00

Many authors have examined various boundary behaviors of univalent harmonic mappings in the open unit disk. Building on the work of Laugesen, Bshouty and others, this paper extends earlier results on the boundary behavior of univalent harmonic mappings under different conditions. We determine the angular limits of the arguments and logarithms of the analytic and co-analytic parts of univalent harmonic mappings in terms of the derivative of the boundary function and the dilatation. Explicit formulas are obtained when this derivative is finite. We also show that the dilatation possesses a finite number of zeros within any Stolz angle provided the derivative of the boundary function tends to infinity. For mappings onto bounded convex domains, the complex derivative has no interior zeros in any Stolz angle. These results explore and complement earlier work and clarify the geometric role of the di- latation near the boundary.

HANKEL DETERMINANT FOR CERTAIN SUBCLASS OF UNIVALENT FUNCTIONS DEFINED BY q-DIFFERENCE OPERATOR

2026-04-16T15:35:40+00:00

The most powerful tool that cannot be completely eroded in the history of Geometric Functions Theory (GFT) is determinant of any order. There is no gaining-saying that determinants have series of applications in Sciences, Engineering, Data analysis, Computing, and generally in other sectors of man’s endeavor. In particular, the Hankel determinant has attracted attention of numerous researchers possibly because of its distinct geometric structural sequence, and despite gaining so much attention there still exist some perceived gaps in knowledge that are yet to be explored. It is on this positive direction that this present study derived its interest so that a new development in knowledge can be reached. The method used the q- Difference Operator with the second Hankel determinant as well as its inverse functions of order two along with the concept of subordination principle. With this approach in focus,this study examined some new subclasses of analytic functions. The sharp initial coefficient bounds obtained were used to derive some new subclasses of the Second Hankel along with its inverse functions.

ON CONVEX p-VALENT FUNCTIONS MAPPED ONTO THE NEPHROID DOMAIN

2026-04-16T15:35:40+00:00

p-valent functions serve as natural generalizations of univalent functions and offer a broad platform for studying geometric and functional properties within complex analysis. While coefficient estimation is a core problem in geometric function theory (GFT), the specific bounds and functional determinants for convex p-valent functions associated with the nephroid domain remain under-explored. This research addresses this gap by investigating a new subclass of functions characterized by subordination to a kidney-shaped region, which is motivated by the need to extend existing univalent results to broader p-valent classes. Using the theory of subordination and Taylor–Maclaurin series expansions, the methodology involves comparing the structural coefficients of convex p-valent functions against the nephroid-type mapping P (ξ) = 1+ξ − ξ³/3 . The author establishes estimates for the initial coefficients |a_1+p| and |a_2+p|, and derives a generalized coefficient bound for |a_n_+p|. These findings are verified for consistency by reducing the results to the specific univalent case where p = 1.

TEMPORAL AND CHANNEL-SPECIFIC PATTERNS IN NIGERIAN FRAUD: INTERPRETABLE MACHINE LEARNING ON A LARGE-SCALE SYNTHETIC DATASET

2026-04-16T15:35:40+00:00

An examination of temporal and channel-specific fraud patterns is conducted using a large-scale synthetic dataset (1 million records) calibrated to Nigerian (NIBSS 2023) fraud distributions. Comparative evaluation of Logistic Regression, Random Forest, and XGBoost models, supported by SHAP interpretability, reveals that the Web (0.34%) and Mobile (0.33%) channels has highest risk. January (0.53%) and 01:00 (0.36%) are identified as peak fraud periods. Analysis confirms that there exist negligible linear correlation between temporal features and fraud, validating the need for non-linear ensemble ap-proaches. The study concludes by proposing an interpretable, channel-aware framework for real-time risk scoring applicable to emerging markets.

A HYBRID APPROACH TO FORECASTING STOCK INDICES USING THE ARMA–GARCH AND ARMA–EGARCH MODELS: EVIDENCE FROM THE NIGERIAN STOCK EXCHANGE

2026-04-16T15:35:40+00:00

The modeling of stock indices on the Nigerian Stock Exchange (NSE) has been carried out using Gaussian-related distributions even when the observed data are not normal. It is necessary to incorporate distributions that are non-normal. Therefore, this study examined the application of clas-sical and hybrid econometric models to forecast the daily movements of the Nigerian Stock Exchange Index (NSE 30). Five competing models were evalu-ated: the Autoregressive Integrated Moving Average (ARIMA), the Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH (EGARCH), and two hybrid extensions that combine mean and variance equations, namely ARIMA–GARCH and ARIMA–EGARCH. Preliminary time–series diagnostics, including stationarity, normality, autocorrelation, and heteroskedasticity tests, revealed that the log–return series is stationary, non–normally distributed, and characterised by conditional volatility clustering. The ARIMA(1,1,2) model, identified through the Akaike Information Criterion, served as the baseline specification for subsequent volatility modelling. Empirical analysis indicates that incorporating volatility dynamics substan-tially enhances forecasting performance. The EGARCH(1,1) model captures leverage effects in the NSE 30 series by giving greater weight to negative shocks, while the symmetric GARCH(1,1) model explains volatility persistence. When combined with ARIMA, both hybrid models deliver the most accurate forecasts, with identical lowest error values, and the DieboldMariano test confirms their clear superiority over the standalone ARIMA model.

A CNN-BASED FRAMEWORK FOR PAYROLL FRAUD DETECTION IN SIMULATED NIGERIAN PUBLIC FINANCIAL DATA

2026-04-16T15:50:15+00:00

This study develops an artificial intelligence–driven framework for detecting payroll fraud in Nigeria’s Public Financial Management (PFM) system using Convolutional Neural Networks (CNNs). The model targets common fraud patterns such as ghost workers, salary inflation, duplicate payments, and payments to retired or overage employees. A dual-stage validation strategy was adopted. First, a publicly available IBM Human Resources dataset containing 1,470 records was used to benchmark the model, achieving an F1-score of 0.87. Second, a realistically simulated Nigerian payroll dataset comprising 12,110 records with 31 features was constructed to reflect local administrative structures and fraud typologies. To address severe class imbalance, the Synthetic Minority Oversampling Technique (SMOTE) was applied during model training. The proposed model demonstrated strong generalization performance on the simulated dataset, achieving an accuracy of 0.958, precision of 0.910, recall of 0.841, F1-score of 0.874, and PR-AUC of 0.857. Furthermore, the trained model was integrated into a real-time fraud alert dashboard to support proactive monitoring and decision-making. The study demonstrates the potential of deep learning approaches for fraud detection using simulated data.