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Research Article
Bivariate Radialsymmetric Kernel Density Estimation of Well-being Distribution and Poverty Index
Youssou Ciss
,
Mamadou Djitan Sinclair,
Mohamed Dinah Bangoura,
Aboubakary Diakhaby
Issue:
Volume 15, Issue 5, October 2026
Pages:
177-201
Received:
9 June 2026
Accepted:
24 July 2026
Published:
5 September 2026
DOI:
10.11648/j.ajtas.20261505.11
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Abstract: In two previous papers, we proposed two bivariate product kernel estimators for the bi-dimensional extension of the Foster, Greer and Thorbecke (FGT) index based respectively on classical and adaptive kernel. The Foster, Greer and Thorbecke (FGT) index was introduced in the literature for the purpose of a dominance approach to multidimensional poverty. The poverty measure utilized in this dominance method is fundamentally a generalization, from one to two dimensions, of this Foster, Greer and Thorbecke index with separate poverty aversion parameters for each dimension. This statistical method (the product kernel estimator) has the following main disadvantes: the curse of dimensionality, the complex selection of the bandwidth, and high computational costs. In this study, we focus on a bivariate radialsymmetric kernel estimator for the bi-dimensional extension of the Foster, Greer and Thorbecke index. Our new bivariate kernel estimator is developed with a classical bivariate kernel of Parzen-Rosenblatt of a probability density function (pdf) utilizing Riemann sums. We next provide complete asymptotic behaviour by establishing both almost-sure uniform and uniform mean square consistencies for the bivariate radialsymmetric kernel estimator. A simulation study indicates that the proposed bivariate kernel estimator performs favorably for small samples comparatively to the bivariate multiplicative kernel estimator.
Abstract: In two previous papers, we proposed two bivariate product kernel estimators for the bi-dimensional extension of the Foster, Greer and Thorbecke (FGT) index based respectively on classical and adaptive kernel. The Foster, Greer and Thorbecke (FGT) index was introduced in the literature for the purpose of a dominance approach to multidimensional pov...
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Research Article
The Accelerated Failure Time Regresssion Model Under the Generalised Gull Alpha Power Log Logistic Distribution for Handling Survival Data in Presence of Covariates
Teresa Wambui*,
Mutua Kilai,
Peter Gachoki
Issue:
Volume 15, Issue 5, October 2026
Pages:
202-212
Received:
3 August 2026
Accepted:
18 August 2026
Published:
11 September 2026
Abstract: This study develops a Generalised Gull Alpha Power Log-Logistic Accelerated Failure Time (GGAPLL-AFT) regression model for analysing censored survival data in the presence of covariates. The model was developed by integrating the Generalised Gull Alpha Power Log-Logistic (GGAPLL) distribution into the Accelerated Failure Time framework, thereby combining the flexibility of the GGAPLL distribution with the interpretability of AFT regression. The proposed model is intended to provide a flexible approach for survival data characterised by different hazard rate structures, including increasing, decreasing, and unimodal hazards. The mathematical formulation of the proposed model was established by deriving its cumulative distribution function, probability density function, survival function, hazard function, and conditional survival function. The AFT formulation relates the logarithm of survival time to a linear function of covariates and a GGAPLL-distributed error term, allowing covariate effects to be interpreted in terms of acceleration or deceleration of survival time. The unknown model parameters were estimated using the Maximum Likelihood Estimation (MLE) method. Since the resulting likelihood equations are nonlinear and do not have closed-form solutions, numerical optimisation was performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The performance of the proposed estimators was evaluated through a Monte Carlo simulation study under increasing, decreasing, and unimodal hazard scenarios. Simulations were conducted for different sample sizes and censoring levels, with estimator performance assessed using Absolute Bias (AB), Root Mean Square Error (RMSE), coverage probability, and Akaike Information Criterion (AIC). The simulation results showed that estimator performance improved as sample size increased, with reductions in bias and RMSE and coverage probabilities approaching the nominal 95% level. These findings demonstrate that the proposed GGAPLL-AFT model provides a flexible and reliable framework for parameter estimation and survival regression under diverse hazard structures.
Abstract: This study develops a Generalised Gull Alpha Power Log-Logistic Accelerated Failure Time (GGAPLL-AFT) regression model for analysing censored survival data in the presence of covariates. The model was developed by integrating the Generalised Gull Alpha Power Log-Logistic (GGAPLL) distribution into the Accelerated Failure Time framework, thereby com...
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Research Article
Modelling Mortality Risk in Malaria Patients Using Logistic Regression Model: A Case Study of Nakuru Level 6 Hospital
Issue:
Volume 15, Issue 5, October 2026
Pages:
213-230
Received:
7 August 2026
Accepted:
19 August 2026
Published:
11 September 2026
Abstract: Malaria remains a major cause of preventable illness and death in sub-Saharan Africa, yet routinely collected hospital data are not consistently integrated into objective tools for identifying patients at greatest risk of death. This study developed and internally evaluated a five-predictor logistic regression model for in-hospital mortality among malaria patients admitted to Nakuru Level 6 Hospital, Kenya. A retrospective observational design was used, drawing on electronic medical records from 1,500 patients admitted between 2020 and 2026. In-hospital death was the binary outcome, with age, sex, parasite density, haemoglobin level, and platelet count included as predictors. Fifty-four patients died, corresponding to a mortality rate of 3.6%. The original prespecified linear model showed strong discrimination (AUC = 0.922), but diagnostic testing identified significant nonlinearity for age, haemoglobin level, and platelet count. These three predictors were therefore refitted using restricted cubic splines while retaining the same five clinical predictors. The corrected nonlinear model significantly improved fit and discrimination, with an apparent AUC of 0.962. Bootstrap validation produced an optimism-corrected AUC of 0.955 and a Brier score of 0.0275, while repeated stratified cross-validation produced an AUC of 0.954 and a Brier score of 0.0273. Calibration intercepts were close to zero, although slopes below one indicated some residual optimism. Parasite density remained positively associated with mortality, sex remained non-significant, and nonlinear relationships were observed for age, haemoglobin, and platelet count. The conventional 0.5 threshold showed poor sensitivity, while lower thresholds improved detection but were not considered clinically established cut-offs. The findings support use of routine hospital data for mortality risk stratification, but external validation, possible recalibration, and prospective evaluation of clinical thresholds and utility are required before implementation in practice.
Abstract: Malaria remains a major cause of preventable illness and death in sub-Saharan Africa, yet routinely collected hospital data are not consistently integrated into objective tools for identifying patients at greatest risk of death. This study developed and internally evaluated a five-predictor logistic regression model for in-hospital mortality among ...
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