Asian Journal of Probability and Statistics

Statistical Modelling of Nigerian Exchange-Rate Volatility Using an Arma–Garch Framework

H. B. Buari — 2026-10-23

This study models daily USD/NGN exchange-rate volatility using an autoregressive moving-average–generalised autoregressive conditional heteroskedasticity (ARMA–GARCH) framework. The analytical series covers December 2024 through July 2026. The imported file contained 403 rows; duplicate-date screening yielded 397 unique exchange-rate observations and 396 percentage log returns. The Augmented Dickey–Fuller test rejected a unit root in the return series (test statistic = −8.6721, p < .001), while ARCH–LM tests at lags 5, 10 and 15 detected conditional heteroskedasticity (all p < .001). Among the reported low-order ARMA candidates, ARMA(2,2) was retained because it was the only specification with a Ljung–Box Q(10) p-value above .05, despite not minimising the information criteria. The reported Gaussian ARMA(2,2)–GARCH(1,1) fit produced ARCH and GARCH estimates of α = 0.366944 and β = 0.316000, giving α + β = 0.682944. This value is below unity and therefore indicates a finite-variance, mean-reverting conditional-volatility process under the fitted specification. Post-estimation ARCH–LM tests did not detect remaining ARCH effects at the examined lags. Point volatility forecasts increased from 0.3598% at one trading day ahead to 0.5058% at ten trading days ahead and approached the model-implied long-run daily volatility of approximately 0.5100% over a 30-trading-day horizon. The findings support the presence of time-varying but mean-reverting USD/NGN volatility during the study window. Because the analysis does not include an out-of-sample forecast-accuracy exercise or coefficient-level inferential statistics, the conclusions are limited to the reported sample, diagnostics and point forecasts.

Weibull Accelerated Failure Time (AFT) Model: The Effect of Socioeconomic and Demographic Factors on Survival Time in Kenya

Levis Otieno Oduori — 2026-10-23

Life expectancy is a fundamental demographic indicator that reflects population health and socio-economic development. However, the effects of socio-economic and demographic covariates on survival time in Kenya have rarely been quantified using fully parametric survival regression models. This study estimated and interpreted the effects of selected covariates on survival time using the Weibull Accelerated Failure Time (AFT) model. Secondary data from the 2022 Kenya Demographic and Health Survey (KDHS), comprising 5,400 adults, were analysed. Candidate predictors were identified through univariable Cox proportional hazards regression and subsequently selected using the Akaike Information Criterion (AIC). Model parameters were estimated using maximum likelihood estimation (MLE). The adequacy of the fitted Weibull AFT model was assessed using Weibull probability plots, Cox-Snell residuals, quantile-quantile (Q-Q) plots, and the Kolmogorov-Smirnov goodness-of-fit test. Regression effects were interpreted using time ratios, where values >1 indicated prolonged survival and values <1 indicated reduced survival time. The fitted model identified educational attainment, household wealth, employment status, sex, and place of residence as statistically significant predictors of survival time (p < 0.05). Higher educational attainment and greater household wealth significantly increased expected survival time, whereas unemployment and male sex significantly accelerated mortality by reducing survival time. Urban residence was associated with a modest increase in survival time relative to rural residence. These findings demonstrate that the Weibull AFT model provides a robust and interpretable parametric framework for quantifying the effects of socio-economic and demographic determinants on life expectancy. The study highlights the utility of time-ratio interpretation in survival modelling and provides empirical evidence to inform policies aimed at reducing health inequalities and improving population longevity in Kenya.

Monte Carlo Assessment of Statistical Process Control and Process Capability under Different Production Conditions: Evidence from Sachet-Water Manufacturing

Mark Clement Ushie — 2026-10-23

Statistical process improvement is frequently inferred from lower defect rates, favourable capability indices, or an absence of control-chart signals, although these indicators address different dimensions of process behaviour and may be affected by sampling variation. This study develops and evaluates a reproducible Monte Carlo framework for examining the operating behaviour of Statistical Process Control (SPC) charts and process capability/performance indices in a simulated sachet-water production system. The simulation followed an Aims–Data-generating mechanism–Estimands–Methods–Performance measures (ADEMP) structure and generated 10,000 independent 60-day production replications. Each replication comprised three shifts per day and 50 sachets per shift (9,000 sachets; 180 rational subgroups). The first 30 days represented a baseline process and the final 30 days an improved process. Fill volume was generated as a continuous quality characteristic, while leakage, printing failure and overall defective status were represented as attribute outcomes. The study evaluated the X-bar and S charts, a p-chart, and the Cp, Cpk, Pp and Ppk indices. Three one-subgroup special causes were also embedded to assess immediate detection: a sealing-temperature drop, a machine-speed surge and a post-improvement fill-volume drift. Under the primary data-generating mechanism, the mean defective-sachet proportion declined from 14.978% to 2.040%, an absolute reduction of 12.938 percentage points and an approximate 86.36% relative reduction. The within-subgroup standard deviation declined from 4.600 to 1.9995 mL, while mean Cpk increased from 0.5435 to 1.6623. All 10,000 replications recovered the expected direction of change for defective proportion, within-subgroup variance and Cpk. Control-chart performance was less uniform: the X-bar chart detected the Day-48 mean shift in 94.60% of replications, whereas the S chart detected the associated dispersion increase in 33.29%; the p-chart detection rate for the Day-12 sealing disturbance was 68.74%. Sensitivity analysis showed that the sustained improvement conclusion remained stable under heavy-tailed errors, autocorrelation, subgroup heterogeneity and attribute overdispersion, but false-alarm and detection characteristics changed materially under dependence and heterogeneity. The findings demonstrate that defect reduction, capability and statistical stability should be interpreted as complementary evidence. The article's primary contribution is methodological: it shows how repeated simulation can distinguish reliable recovery of known process changes from the less certain detection of short-lived disturbances.

Development of a Hierarchical Multilevel Logistic Regression Model for Predicting Maternal Mortality in Kenya

Doreen Wanjue Muverethi — 2026-10-24

Aim: To develop and evaluate a hierarchical multilevel logistic regression model for predicting maternal mortality in Kenya.
Methodology: Secondary data from the Kenya Demographic and Health Survey (KDHS) (2022), Kenya Population and Housing Census (KPHC) (2019), and national health registries for 2018–2023 were combined, yielding a sample of 32,156 women aged 15–49 years. Random Forest was used for variable selection, followed by two-level logistic regression modelling. Model performance was assessed using the Akaike information criterion (AIC), the Bayesian information criterion (BIC), likelihood-ratio tests (LRT), and repeated 10-fold cross-validation.
Results: The null model indicated significant between-county variation (ICC = 8.2%), supporting the use of a multilevel approach. The final model showed good fit (AIC = 3,498.1; marginal R^{2}=16.6\%; conditional R^{2}=24.7\%). Higher education reduced the odds of maternal mortality by up to 75%, while each additional antenatal care (ANC) visit reduced the odds by 15%. In contrast, high parity (OR = 1.26), greater distance to health facilities (OR = 1.02 per km), and county poverty rate (OR = 1.03) significantly increased mortality risk. The model demonstrated acceptable predictive performance (AUC = 0.78), with specificity of 88.9%. The confusion matrix is based on pooled out-of-fold predictions across all five repetitions of 10-fold cross-validation. In the internal validation set, the model showed limited sensitivity for maternal death (36.4%; 4/11) and very low PPV (1.1%), indicating limited case-detection performance at the selected threshold in this rare-outcome dataset.
Application: The preliminarily developed and internally assessed multilevel predictive model provides a framework for population-level risk stratification. It may inform county health management teams about the equitable allocation of maternal healthcare resources, such as targeted deployment of community health promoters and emergency transport subsidies to high-poverty counties.
Conclusion: These findings highlight the importance of accounting for both individual- and county-level factors in maternal mortality research and support targeted interventions focused on improving female education, ANC, and equitable resource allocation in high-poverty counties. The consistent reductions in information criteria, coupled with significant LRTs at each modeling stage, substantiate that maternal mortality in Kenya is best understood through a multilevel analytical framework. The model’s acceptable discriminative performance (AUC = 0.78) and satisfactory calibration indicate that it distinguishes between high-risk and low-risk profiles while maintaining probabilistic accuracy across the predicted risk spectrum. However, the model requires external validation before clinical or operational use.

Generative Adversarial Network Augmentation of Whole-Blood Raman Spectra for Breast-Cancer Classification: A PCA–LDA and Patient-Aware Validation Study

Brian O. Mairura — 2026-10-26

Background: Whole-blood Raman spectroscopy provides a label-free molecular fingerprint with potential for breast-cancer classification, but limited sample sizes and substantial biological variability can restrict model generalization. This study evaluated whether generative adversarial network (GAN) augmentation could improve PCA–LDA classification while preserving patient-independent evaluation.

Methods: Whole-blood Raman spectra from breast-cancer patients and healthy controls across Stages I–III were analysed using PCA–LDA under four data-composition scenarios: RealOnly, Real25, Real50 and Real100, corresponding to 0%, 25%, 50% and 100% synthetic augmentation. Vanilla GAN and conditional GAN (cGAN) data were evaluated using SpectrumKFold, SubjectKFold and leave-one-patient-out cross-validation (LOPOCV). Classification performance was assessed using accuracy, sensitivity, specificity, balanced accuracy, F1-score, MCC and ROC-AUC, with spectral correspondence and prediction confidence additionally examined.

Results: Spectrum-level validation frequently produced near-perfect discrimination, whereas patient-aware validation produced more conservative performance, demonstrating the influence of inter-patient variability. GAN augmentation generally improved sensitivity, balanced accuracy, F1-score and MCC, with the largest benefits observed for the more challenging patient-aware settings. cGAN generally produced greater improvements than vanilla GAN and frequently achieved strong performance at lower augmentation levels. Under LOPOCV, for example, Stage II sensitivity increased from 79.09% with real data alone to 87.32% with 25% cGAN augmentation, while Stage III sensitivity increased from 75.23% to 82.98%. Stage III remained the most challenging setting, with RealOnly LOPOCV AUC of 0.9521 compared with 0.9918 for Stage II.

Conclusion: GAN-based augmentation can strengthen PCA–LDA classification of whole-blood Raman spectra, particularly for patient-aware detection of breast-cancer spectra. cGAN showed greater augmentation efficiency than vanilla GAN in several settings. However, the small number of patients within individual stages and absence of independent external validation limit generalizability. Larger multicentre datasets and external validation are required before clinical applicability can be established.

Bayesian Structural Time Series Modelling of Monthly Petroleum Product Sales in Plateau State, Nigeria

H. Ali — 2026-10-27

Monthly petroleum-product sales can vary with seasonal activity, market conditions, and distribution constraints. This study examines reported monthly sales volumes of Premium Motor Spirit (PMS) and Automotive Gas Oil (AGO) at plateau state petroleum-products distribution depot in Nigeria, using 72 observations for each product from January 2020 to December 2025. Exploratory plots, seasonal-trend decomposition, and Bayesian structural time-series (BSTS) summaries were assessed alongside alternative structural and autoregressive specifications. The basic BSTS summaries reported coefficients of determination of 0.6976 for PMS and 0.3821 for AGO. Posterior medians for the tabulated autoregressive coefficients were -0.1437 for PMS and -0.4899 for AGO, although both 95% credible intervals included zero. Model-comparison summaries varied across specification groups, and identical reported AR(1) and AR(2) outputs did not establish an independent advantage for the higher-order model. Ljung-Box results for the autoregressive specifications showed residual serial dependence at 12 and 24 months (PMS: p = 0.022 and 0.0005; AGO: p = 0.0020 and 0.0002). The analyses describe substantial temporal variation in depot sales and illustrate the interpretation of Bayesian structural-model output. Persistent residual dependence, limited seasonal replication, differences among model-summary blocks, and the absence of held-out predictive evaluation restrict conclusions about forecast performance and operational usefulness.

A Bayesian Panel Vector Autoregression Modelling of Macroeconomic Linkages and Shock Transmission in Kenya’s Pension Sector

George Mbayachi Shiro — 2026-10-27

Background: The modern architecture of retirement benefit schemes in Kenya has undergone profound structural evolution over the past two decades, surpassing KES 2.531 trillion in assets under management, with a pension-to-GDP ratio of approximately 14.6%. While institutional governance dictates internal micro-efficiency, systemic pension fund performance remains inherently tethered to exogenous macroeconomic shocks.

Aims: This study evaluated the long-run equilibrium relationships and structural shock transmission between the Kenyan pension sector and key macroeconomic aggregates (real GDP, consumer price inflation, and 91-day Treasury bill rates) over a two-decade horizon (2005–2024).

Study Design: A quantitative research design was used.

Duration of Study: The study covered a two-decade horizon (2005–2024).

Methodology: Using Johansen co-integration tests and a Hierarchical Bayesian Panel Vector Autoregression (BPVAR) model equipped with Minnesota shrinkage priors (λ=0.259), the study investigated multivariate co-integration properties and dynamic causal mechanisms. The Johansen trace test results (r=0, trace statistic of 52.79 versus a critical value of 53.12 at the 5% significance level) indicated the absence of a long-run co-integrating vector among the variables, supporting the use of the BPVAR in first differences.

Results: Markov Chain Monte Carlo (MCMC) convergence diagnostics, based on 15,000 iterations, a thinning factor of 5, a high acceptance rate of 94.6%, and a posterior marginal likelihood of -173.919, indicated structural stability. Structural Impulse Response Functions (IRFs) and Forecast Error Variance Decompositions (FEVDs) revealed a pronounced “Macro-Tether”: inflationary shocks function as a systemic tax, accounting for approximately 60% of the observed volatility in pension Return on Assets (ROA). Posterior predictive checks indicated high predictive accuracy, showing that, while individual schemes maintain an internal governance floor, aggregate sectoral returns are structurally conditioned by macroeconomic cycles.

Conclusion: These findings provide empirical evidence that may inform macroprudential regulators at the Retirement Benefits Authority (RBA) in safeguarding systemic financial stability.

A Simulation and Real-Data Evaluation of Causal Discovery Algorithms under Realistic Social Science Conditions

Sacha Varin — 2026-10-30

Background: Causal discovery algorithms aim to infer causal structure from observational data under explicit assumptions, yet their performance under realistic social science conditions remains insufficiently understood. Existing evaluations typically rely on large samples, high-dimensional settings, and clean data—conditions that rarely hold in applied research.

Objectives: This study evaluates four base algorithms (PC, GES, FCI, GFCI_approx) and three bootstrap-enhanced variants (FGES_boot, GFCI_approx_boot, FCI_boot) under conditions intended to reflect constraints commonly encountered in applied social science research, with the aim of understanding how different causal discovery methods behave under realistic small-sample, low-dimensional, and imperfect-data conditions.

Methodology: Algorithms were evaluated through a factorial simulation design spanning small sample sizes (N = 25–200), low dimensionality (p = 4–6), moderate outlier contamination, and moderate departures from linearity (20% of causal relationships generated using quadratic functions), complemented by an illustrative application to a real educational dataset (35 countries × 7 indicators). GFCI_approx is a custom hybrid causal discovery method inspired by selected components of the GFCI framework (Ogarrio et al., 2016); because it replaces the FGES search phase with hill-climbing optimization, it should be interpreted as a distinct hybrid method rather than an implementation of the original GFCI algorithm.

Findings: Five main findings emerged. First, all algorithms exhibited a pronounced precision–recall asymmetry, with consistently higher precision (0.92–1.00) than recall (0.43–0.91) across the examined conditions. Second, recovery performance improved substantially between N = 50 and N = 100, while estimation uncertainty decreased and performance became more stable at larger sample sizes. Third, increasing dimensionality (p = 4 to 6) reduced recovery accuracy unless compensated by larger sample sizes. Fourth, moderate outlier contamination reduced performance by approximately 5–22%, whereas the moderate departures from linearity examined in this study had only a negligible effect (approximately 1.6%), indicating that outlier contamination was the dominant source of performance degradation. Fifth, an illustrative application to a real educational dataset showed that, after removal of a composite variable, PC and FCI converged on two undirected edges; bootstrap stability analysis provided stronger support for the Effectiveness–Equity edge (stability = 0.800, 95% CI [0.657, 0.943]) than for the Parent engagement–Effectiveness edge (stability = 0.733, 95% CI [0.575, 0.892]). Because no ground-truth causal structure is available, this application should be interpreted as an illustration of the proposed workflow rather than as a validation of recovered causal relationships.

Conclusion & Implications: We provide practical recommendations regarding sample size, preprocessing, and robustness assessment, and argue that causal discovery in small-sample social science settings is best viewed as a conservative hypothesis-generation and filtering tool rather than a comprehensive structure recovery method. By aligning the simulation design with realistic applied constraints, this study helps bridge the gap between methodological research and empirical practice.

A Novel Group Runs Control Chart for Monitoring Simple Linear Profiles Using Modified Hotelling’s T2 Statistic

Piyush Shaha — 2026-10-31

Profile monitoring is an important area of statistical process monitoring, particularly when the quality of a process is characterised by the relationship between a response variable and one or more explanatory variables. Although synthetic control charts have been developed for monitoring linear profiles, there is scope for improving their ability to detect shifts in process parameters. This paper proposes a novel Group Runs (GR) control chart based on the modified Hotelling’s (T²) statistic for Phase II monitoring of simple linear profiles. The proposed chart integrates the modified (T²) statistic with the Group Runs monitoring scheme to enhance the detection of changes in the parameters of a simple linear profile. The performance of the proposed GR-modified (T²) control chart is evaluated and compared with that of the existing synthetic-modified (T²) control chart under different shift scenarios. The comparative results, assessed in terms of average run length (ARL), demonstrate that the proposed Group Runs chart performs better than the synthetic-modified (T²) chart in detecting small shifts in simple linear profiles. It is also observed that the existing synthetic modified (T²) control chart is better than the proposed GR modified (T²) control chart in detecting larger shifts. The proposed scheme therefore provides an effective alternative for Phase II profile monitoring and contributes to the development of more sensitive control charting techniques for statistical process control.

Length-Biased Slash-Exponential-Frechet Distribution: Statistical Properties, Estimation and Application

Benjamin Apam — 2026-11-02

Aims: To construct the length-biased slash-exponential-Fréchet (LB-SEFr) distribution, establish its principal distributional and tail properties, and assess its ability to represent positively skewed lifetime observations.
Study Design: A methodological investigation combining mathematical derivation, Monte Carlo simulation, and a comparative application to observed survival times.
Place and duration of study: The theoretical and computational investigations were conducted in Ghana; the empirical application uses historical animal survival observations.
Methodology: The LB-SEFr model was obtained by weighting the SEFr density in proportion to survival duration under the finite-mean constraint \(\lambda>1\). Density, distribution, reliability, moment, quantile, and related functional properties were examined.
Maximum-likelihood estimation was assessed in 1,000-replication Monte Carlo simulations for four parameter settings and sample sizes of 100,300 , and 500 . Empirical fit was compared with six alternative distributions using likelihood-based criteria and empirical-distribution discrepancies for 72 guinea-pig survival observations.
Results: Optimization convergence ranged from \(98.2 \%\) to \(100 \%\). Bias and root mean squared error generally decreased with sample size, although estimation of the additional shape parameter was unstable in some smaller samples. The fitted parameters were \(\widehat{\sigma}=75.4111, \widehat{\lambda}=3.0044\), and \(\widehat{\alpha}=0.4589\). LB-SEFr had the smallest AIC (783.781), AICc (784.134), Kolmogorov-Smirnov discrepancy (0.0708), Cramér-von Mises discrepancy (0.0638), and Anderson-Darling discrepancy (0.4152). The lognormal model had a smaller BIC (789.224 compared with 790.611).
Conclusion: The LB-SEFr distribution is a mathematically well-defined and empirically competitive heavy-tailed lifetime model. The observed sample does not establish a length-biased selection process, and further evaluation under documented length-biased and censored sampling designs is warranted.

Estimation of the Parameters of Power Exp-Gamma Distribution and Its Applications

N. R. Bhandale — 2026-11-05

This study introduces the Power Exp-Gamma (PEXPG) distribution by applying a power transformation to the Exp-Gamma model. The probability density and cumulative distribution functions are obtained, and selected statistical properties relevant to lifetime modelling are examined. These include raw moments and associated measures, the moment-generating, characteristic and cumulant-generating functions, order statistics, and the survival, hazard and reverse hazard functions. The density is also represented as a two-component mixture involving Weibull and generalised gamma distributions. The parameters are estimated by maximum likelihood, and the resulting likelihood equations are addressed iteratively using Fisher's scoring method in R. A simulation study considers three parameter combinations, sample sizes of 50, 100, 150 and 200, and 10,000 replications. The reported mean squared errors decrease with increasing sample size across the configurations examined. Model applicability is assessed using four datasets comprising annual maximum precipitation, breast cancer survival times, censored reliability failure times and recidivism failure times. The PEXPG model is compared with the power Akash, power Amarendra, power Ishita and power Sujatha distributions using the Akaike and Bayesian information criteria and the Kolmogorov–Smirnov statistic. The reported goodness-of-fit results favour PEXPG for all four datasets examined. The distribution also exhibits different hazard-rate patterns across parameter settings, indicating flexibility within the cases studied. These findings support further evaluation of PEXPG as an alternative model for the types of data considered.

Bayesian Logistic Classification of Synthetic Cholera-related Profiles: A Methodological Simulation Study

L. A. Bichanga — 2026-11-09

Background: Some correctional facilities may face an elevated risk of cholera transmission when population density, limitations in water and sanitation infrastructure, and restricted access to timely healthcare occur concurrently. Statistical classification can support methodological development, but simulated analyses must be distinguished from empirical outbreak forecasting.

Methods: A synthetic dataset of 10,000 profiles was generated from ten coded variables representing symptoms, demographic characteristics, water exposure, and environmental conditions. Binary outcomes labelled as susceptible or infected were drawn from a prespecified logistic data-generating model. Regression coefficients were estimated in a Bayesian framework using a random-walk Metropolis-Hastings algorithm with 10,000 iterations and a 1,000-iteration burn-in. Posterior mean probabilities were dichotomised at 0.50, and internal performance was examined using an 80:20 training-test split.

Results: Posterior estimates were generally close to their prespecified generating values, with a mean absolute error of 0.070 and a root-mean-square error of 0.095. All reported 95% credible intervals excluded zero; this result was expected because the simulation used non-zero coefficients and a large sample. Test-set accuracy was 96.60% and sensitivity was 99.37%, but specificity was 41.67% and balanced accuracy was 70.52%. The positive-class prevalence in the test set was 95.20%, so overall accuracy substantially reflected class imbalance.

Conclusion: The analysis demonstrates parameter recovery and internal classification behaviour under a correctly specified synthetic model. It does not estimate a dynamic susceptible-infected-recovered process, establish clinical diagnosis, or validate outbreak prediction in real correctional populations. Empirical longitudinal data, laboratory-confirmed outcomes, multi-chain Bayesian diagnostics, calibration assessment, and external validation are required before operational use.

Structural Breaks and Comparative Time-Series Forecasting of Kenya’s Mobile Money Ecosystem

Lali Yusuf Ali — 2026-11-10

Background: Kenya’s mobile money ecosystem has expanded substantially, but changes in its underlying growth rate and the forecasting implications of those changes warrant examination.

Problem: Policy-associated movements in the aggregate series may reflect longer-running structural changes rather than effects attributable to a particular intervention.

Aim: To detect structural breaks, assess the March 2020 emergency period and compare transaction-volume forecasts across horizons.

Methods: Monthly Central Bank of Kenya statistics covering July 2009–April 2026 (202 observations) were analysed. Chow, sup-F, dynamic-programming, CUSUM and variance-break tests examined stability. Seasonal ARIMA intervention models estimated adjusted period associations. Eight forecasting models were compared using expanding-window rolling-origin evaluation at 1-, 3-, 6- and 12-month horizons.

Results: Transaction-volume growth changed in May 2017 (sup-F = 13.72, P = .001), declining from approximately 2.2% to 0.5% monthly. CUSUM crossed its lower bound in June 2018; no robust variance break was identified. During March–December 2020, volume was 4.8% below its model-implied path (P = .006). The April–May 2020 window yielded a 13.1% reduction. Value and ticket-size effects were not statistically significant. Damped-trend exponential smoothing had the lowest forecast errors at every horizon (MAPE approximately 2.3%–3.1%).

Conclusion: Transaction-volume growth slowed before the 2018 policy changes, precluding attribution of the earlier break to those measures. The 2020 contraction was temporary, and forecast accuracy depended on accommodating trend deceleration.