Asian Journal of Probability and Statistics

Prediction of Monthly Incidence of Malaria for Students in A University Clinic

2026-07-28T11:47:56+00:00

This study analysed the monthly incidence of malaria diagnosed among students who visited a university clinic for medical check-ups over a five-year period (2019-2023). The data were examined using graphical methods and a discrete-time Markov chain model. Monthly totals were classified into five discrete incidence states, and the transition probabilities between pairs of states were estimated. The Chapman-Kolmogorov equations were used to obtain n-step transition probabilities, while steady-state probabilities were determined using both repeated matrix multiplication and steady-state equations. The model was then used to predict future monthly malaria incidence levels among students attending the clinic. The results showed that the highest annual incidence of diagnosed malaria during the study period occurred in 2023. The findings also indicated a higher likelihood of increased malaria incidence from October to January of the following year. The first incidence state, representing 1-50 diagnosed students per month, was the most likely to dominate in the long run if prevailing conditions remained unchanged, accounting for approximately 57% of monthly diagnosed malaria totals at steady state. The analysis further suggested that the Markov process would most likely reach steady state after 41 months. These findings provide an incidence-level forecasting framework for clinic-based malaria planning within the study setting.

Sectoral Segmentation and Classification in Emerging Economies: A Multivariate Analysis Framework

2026-07-28T12:46:14+00:00

Emerging economies are increasingly recognised as key contributors to global economic growth; however, their sectoral structures often remain uneven and characterised by significant imbalances. This study examines the segmentation and classification of economic sectors in emerging economies using an integrated multivariate analytical framework. Specifically, it combines factor analysis, principal component analysis (PCA), cluster analysis and discriminant analysis to uncover underlying patterns, reduce data complexity and identify distinct sectoral groupings. Using secondary macroeconomic data on key indicators, including gross domestic product (GDP), employment, investment, infrastructure and trade performance, the analysis reveals a dominant economic dimension largely driven by investment and government expenditure. The results further identify three distinct sectoral clusters representing high-performing, moderately performing and low-performing sectors, thereby highlighting the heterogeneous nature of economic structures in emerging markets. Discriminant analysis supports the robustness of these classifications, with tourism, investment and public expenditure emerging as key variables influencing sectoral differentiation. The findings underscore the limitations of traditional broad sector classifications and demonstrate the value of multivariate techniques in providing deeper insights into economic structures. The study concludes that emerging economies exhibit uneven development, with growth concentrated in specific sectors without corresponding improvements in others. Accordingly, it advocates cluster-based policy approaches, increased investment in social and infrastructure sectors and strategic diversification to support more balanced and sustainable economic development.

Construction of a Thirty-Three-Point Second-Order Rotatable Design in Three Dimensions Using Trigonometric Functions

2026-07-29T06:19:18+00:00

Response surface methodology (RSM) is a collection of mathematical and statistical tools intended for analysing experiments in which a response is influenced by one or more controllable variables. The construction of second-order rotatable designs (SORDs) frequently requires substantial resources, making such designs inefficient and expensive to implement. Consequently, it is important to use an appropriate design that allocates a relatively small number of design points to the elements of interest in the response. The objective of this study was to develop a rotatable design in three dimensions using trigonometric functions. The specific objectives were to construct a modified second-order rotatable design in three dimensions, assess the performance of the constructed SORD using D-, A-, E-, T-, and G-optimality criteria, and examine its relative efficiencies. The reduced SORD was constructed by selecting part of a suitable set of existing design points while keeping the other set constant. The resulting points were subjected to the moment and non-singularity conditions required for second-order rotatability. The alphabetic optimality criteria (A-, D-, E-, T-, and G-) were evaluated using the full parameter system of interest. An optimality criterion is a scalar measure that summarises the quality of a design and is maximised or minimised according to the criterion under consideration.

Hierarchical Clustering of Indian States Based on Child Mortality Indicators: Evidence from NFHS-5

2026-07-31T08:08:56+00:00

Background: Child mortality remains a critical public health concern in India, with substantial disparities in infant, child, and under-five mortality across states.

Aims: The study aims to classify Indian states according to their child mortality profiles using hierarchical cluster analysis based on infant mortality rate (IMR), child mortality rate (CMR), and under-five mortality rate (U5MR), and to identify regional patterns that may support targeted public health interventions.

Study Design: Cross-sectional analytical study using secondary data.

Place and Duration of Study: The study was conducted using state-level data from the National Family Health Survey-5 (NFHS-5), India (2019–2021). The analysis was carried out during 2026.

Methodology: State-level estimates of IMR, CMR, and U5MR for 30 Indian states were analysed. Descriptive statistics and Pearson's correlation analysis were performed to examine the distribution and relationships among the mortality indicators. The variables were standardised using a Z-score transformation, and Mahalanobis distance was used to assess multivariate outliers. Hierarchical agglomerative cluster analysis using Ward's minimum variance method and Euclidean distance was performed. The Elbow method was used to determine the optimal number of clusters. The cluster solution was validated using one-way analysis of variance (ANOVA) and Tukey's Honest Significant Difference (HSD) test. Spatial distribution maps and boxplots were used to visualise regional mortality patterns.

Results: The Elbow method identified a three-cluster solution. Cluster 1 included 19 states with intermediate mortality levels, Cluster 2 comprised 4 states with the lowest mortality, and Cluster 3 contained 7 states with the highest mortality. Significant differences were observed among the clusters for IMR (F = 38.21, P < .001), CMR (F = 16.77, P < .001), and U5MR (F = 44.81, P < .001). The spatial distribution of the clusters revealed marked regional disparities, with high-mortality states predominantly concentrated in northern and central India.

Conclusion: Hierarchical cluster analysis successfully classified Indian states into statistically distinct child mortality groups. The identified clusters provide a practical framework for region-specific public health planning, efficient resource allocation, and targeted interventions aimed at reducing child mortality and regional inequalities across India.