Alexander Boateng

This paper applies the von Mises family of circular distributions to model seasonal timing of heavy rainfall extremes in Kimberley, South Africa. Unlike conventional modelling approaches that emphasize the modelling of mean rainfall, circular modelling captures phase-specific characteristics, such as the onset, peak clustering, and transitional shoulders of extreme rainfall. We consider three variants of the von Mises family of distributions, namely the standard von Mises, generalized von Mises, and sine-skewed von Mises, and then use the maximum likelihood estimation with box-constrained optimization to estimate parameters. The results show that the standard von Mises distribution consistently outperforms more complex alternatives, thus providing the most parsimonious and reliable representation of Kimberley’s summer rainfall regime. Furthermore, the results reveal a dominant seasonal peak in January–February, a recurrent onset in November, and a dry season in June–July, which confirms the episodic and clustered nature of rainfall in semi-arid regions. Phase-shift analyses further indicate that there is approximately a 19-day delay in the seasonal peaks between baseline and monitoring periods, alongside stronger clustering of extremes. Although formal circular tests did not detect statistically significant differences, the phase analysis highlights emerging tendencies toward a later and more compressed rainfall season. These findings have practical implications for flood preparedness, reservoir operations, and agricultural scheduling, where timing rather than totals drives risk and resilience. This study demonstrates the methodological importance of circular statistics in extreme rainfall phase analysis, thus bridging a critical gap in semi-arid climate studies.

Classical binomial interval methods often exhibit poor performance when applied to extreme conditions, such as rare-event scenarios or small-sample estimations. Recent frequentist and Bayesian approaches have improved coverage in small samples and rare events. However, they typically rely on fixed error margins that do not scale with the magnitude of the proportion. This distorts uncertainty quantification at the extremes. As an alternative method to reduce these boundary distortions, we propose a novel hybrid approach. It blends Bayesian, frequentist, and approximation-based techniques to estimate robust and adaptive intervals. The variance incorporates sampling variability, Wilson score margin of error, a tuned credible level, and a gamma regularization term that is inversely proportional to sample size. Extensive simulation studies and real-data applications demonstrate that the proposed method consistently achieves better coverage proportions at all sample sizes and proportions. It provides more conservative interval widths below a sample size of 50 and competitively narrower widths from moderate to large sample sizes, especially beyond 50, compared to the Jeffreys’ and Wilson score intervals. Geometric analysis of the tuning curves demonstrates how the blended method adaptively tunes credible levels across binomial extremes. It starts at higher values for small samples and gradually flattens into near-linear, symmetric trajectories as sample size increases. This ensures robust coverage and balanced sensitivity. Our method offers a theoretically grounded, computationally efficient, and practically robust estimation of rare-event intervals. These intervals have applications in safety-critical reliability, epidemiology, and early-phase clinical trials.

Classical binomial interval methods often exhibit poor performance when applied to extreme conditions, such as rare-event scenarios or small-sample estimations. Recent frequentist and Bayesian approaches have improved coverage in small-samples and rare-events but typically rely on fixed error margins that do not scale with the magnitude of the proportion, thus distorting uncertainty quantification at the extremes. As an alternative method to reduce these boundary distortions, we propose a novel hybrid approach that blends Bayesian, frequentist, and approximation-based techniques to estimate robust and adaptive intervals. The variance incorporates sampling variability, Wilson score margin of error, a tuned credible level, and a gamma regularisation term that is inversely proportional to sample size. Extensive simulation studies and real-data applications demonstrate that the proposed method consistently achieves competitive or superior coverage proportions with narrower or more conservative interval widths compared to Jeffreys and Wilson score intervals, especially for rare and extreme events. Geometric analysis of the tuning curves reveals convex-to-linear transitions and mirrored symmetry across the rare-extreme spectrum, which underscores its boundary sensitivity and adaptivity. Our method offers a theoretically grounded, computationally efficient and practically robust estimation of rare-event intervals which has applications in safety-critical reliability, epidemiology, and early-phase clinical trials.

Background: The coronavirus disease 2019 (COVID-19) pandemic has placed the psychological functioning of mental healthcare practitioners under severe strain. Coping methods may affect mental health outcomes.Aim: The study examined the relationship between depression, anxiety, stress, and coping styles utilised by mental healthcare practitioners during the COVID-19 pandemic.Setting: Three private and one public mental healthcare facility in Bloemfontein, South Africa.Methods: Respondents completed the Depression, Anxiety and Stress Scale (DASS-21) and Brief Coping Orientation to Problems Experienced (Brief-COPE) inventories. An ordinal regression model was used to assess the relationship between coping styles, anxiety and depression.Results: A total of 212 practitioners were included in the analysis. According to DASS-21 measures, approximately 41% and 28% of respondents had moderate to severe depressive and anxiety symptoms, respectively, with the highest prevalence among younger female respondents and nurses. The association between stress severity, anxiety and depression was significant. Avoidant coping methods and two approach coping strategies (planning and acceptance) were associated with depression and anxiety. Anxiety was linked to an increased likelihood of transitioning to higher avoidant categories, while participants with depression were less likely to move to higher avoidant or approach categories.Conclusion: Mental healthcare practitioners, especially nurses, experienced significant COVID-19-related psychological distress during the pandemic. Avoidant coping mechanisms may increase the risk of poor mental health outcomes.Contribution: This study added data on the mental health effects of COVID-19 on mental healthcare practitioners, as well as psychological methods used to cope during the pandemic.