The research was to ascertain the mediating effect of students’ perception in the relationship between the history of mathematics, peer-assisted learning, and students’ interest in mathematics. The study was based on 394 students from four selected secondary schools in the Ashanti region of Ghana. The study was a survey, adopting a structured questionnaire as the research instrument. Structural equation modelling was estimated using Amos (v.23) software, to test the hypothesized paths. History of mathematics had no direct effect on students’ perception towards mathematics, thereby, students’ perception acted as a full mediating variable. Peer-assisted learning had a direct effect on students’ perception towards mathematics, thereby, students’ perception acted as a partial mediating variable. It is recommended to the Ghana Education Service and the Ministry of Education to inculcate the use of history mathematics, as part of the courses in training mathematics teachers.

Hotspot analysis of spatial attributes is a persistent research field in data mining, and applying a model-based clustering procedure is increasingly becoming popular in identifying trends and patterns in datasets on crime events occurring in space. The distributions of potential crime hotspots are parameterized as arising from Gaussian multivariate distributions, whose parameters are estimated by the expectation–maximization (E-M) algorithm, an iterative process with convergence very sensitive to initializations. In this study, a model-based clustering algorithm is explored from the E-M algorithm, initialized by K-means clustering using geodesic distance classification to estimate the model parameters and compared with the classical E-M algorithm, initialized with hierarchical clustering, to identify the distributional patterns of incidence of criminal activities. These model-based clustering algorithms were demonstrated on an open-source large dataset of violent crime activities, which occurred in West Midlands County. Training the data as a Gaussian process, the study identified 12 hotspots of Gaussian mixed models as clusters of an ellipsoidal distribution varying in shape, volume, and orientation, which are mostly found in central parts of boroughs of the study area. The proposed model-based clustering of the E-M algorithm combined with K-means clustering algorithm proved efficient as being fast and stable in convergence with low probability of uncertainty by classifications, producing same classification in some cases when compared to that of the classical E-M and K-means algorithms. The combined model-based clustering techniques applied in the hotspot analysis of criminal activities in space will not only provide insight into crime prediction and resource allocation in combating strategies but also guide researchers to adopt mechanisms for modeling large spatial attributes in data mining.

Several standard distributions can be used to model lifetime data. Nevertheless, a number of these datasets from diverse fields such as engineering, finance, the environment, biological sciences, and others may not fit the standard distributions. As a result, there is a need to develop new distributions that incorporate a high degree of skewness and kurtosis while improving the degree of goodness-of-fit in empirical distributions. In this study, by applying the T-X method, we proposed a new flexible generated family, the Ramos-Louzada Generator (RL-G) with some relevant statistical properties such as quantile function, raw moments, incomplete moments, measures of inequality, entropy, mean and median deviations, and the reliability parameter. The RL-G family has the ability to model right, left, and symmetric data as well as different shapes of the hazard function. The maximum likelihood estimation (MLE) method has been used to estimate the parameters of the RL-G. The asymptotic performance of the MLE is assessed by simulation analysis. Finally, the flexibility of the RL-G family is demonstrated through the application of three real complete datasets from rainfall, breaking stress of carbon fibers, and survival times of hypertension patients, and it is evident that the RL-Weibull, which is a special case of the RL-G family, outperformed its submodels and other distributions.

This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.

Identifying the most parsimonious model in structural equation modelling is of utmost importance and the appropriate power estimation methods minimize the probabilities of Type I and Type II errors. The power of a test depends on the sample size, Type I error, degrees of freedom and effect size. In this study, a modified approach of using effect size in calculating the non-centrality parameter for power is proposed. This is compared to the approach in Maccallum et al. (1996) at different degrees of freedom and sample size specifications --- taken from 50 to 2000. As the sample size increased the difference between the power of a test for both methods reduced to zero. The results showed that the values for power of a test are the same for the modified and original approaches for large sample sizes and degrees of freedom. The findings also revealed that the sample discrepancy function ($\hat{F}$) is asymptotically unbiased.

Probability distributions offer the best description of survival data and as a result, various lifetime models have been proposed. However, some of these survival datasets are not followed or sufficiently fitted by the existing proposed probability distributions. This paper presents a novel Kumaraswamy Odd Ramos-Louzada-G (KumORL-G) family of distributions together with its statistical features, including the quantile function, moments, probability-weighted moments, order statistics, and entropy measures. Some relevant characterizations were obtained using the hazard rate function and the ratio of two truncated moments. In light of the proposed KumORL-G family, a five-parameter sub-model, the Kumaraswamy Odd Ramos-Louzada Burr XII (KumORLBXII) distribution was introduced and its parameters were determined with the maximum likelihood estimation (MLE) technique. Monte Carlo simulation was performed and the numerical results were used to evaluate the MLE technique. The proposed probability distribution's significance and applicability were empirically demonstrated using various complete and censored datasets on the survival times of cancer and diabetes patients. The analytical results showed that the KumORLBXII distribution performed well in practice in comparison to its sub-models and several other competing distributions. The new KumORL-G for diabetes and cancer survival data is found extremely efficient and offers an enhanced and novel technique for modeling survival datasets.