A formula for the confidence interval of correlation coefficient based on the Fishers’ z-transformation, (where z = arctanh(r) and is used to convert the skewed distribution of sample correlation, r to a normal distribution) was applied to the age and systolic blood pressure of 20 individuals. Confidence intervals using percentile and bias-corrected and accelerated (BCa) bootstrap with 2000 replications were also obtained for the same sample sizes respectively. The interval lengths from the derived formula are 0.5997, 0.5073 and 0.3297 for 20, 30 and 50 observations respectively. The interval lengths from the percentile bootstrap are 0.6223, 0.5303 and 0.3077, while interval lengths from BCa bootstrap are 0.6214, 0.4958 and 0.3031 respectively. The interval length decreases as the sample size increases, giving a more accurate confidence interval. The derived formula gives a slightly shorter interval length for n = 20.
The paper presents a multi-infections system model to study the transmission dynamics of Malaria, Zika-Virus and Elephantiasis in an endemic region such as Kedougou in the Southeastern part of Senegal and other parts of the world where it is possible to have multi-infections of the three diseases simultaneously. We performed the disease-free equilibrium and it is shown to be globally asymptotically stable when the associated threshold known as the basic reproduction number for the model is less than unity. Investigation on the existence and stability of equilibria is also performed, the model is found to exhibit backward bifurcation so that for less than unity is not sufficient to eradicate the disease from the population and there is the need to lower below a certain threshold for effective disease control. Sensitivity analysis is performed to determine parameters that have high influence on the basic reproduction number.
Clustering is an unsupervised method where the number of clusters is not known by users. Therefore, the outcomes of a clustering algorithm depend on the input number of clusters specified by users. Consequently it is very important to evaluate the result of the clustering algorithms according to the number of clusters and choose the one that optimize a certain criterion. We present in this paper several clustering validity indices used in the literature. Using several synthetic and real datasets, these indices are then compared based on clustering results provided by the well known k-means clustering algorithm and its non-linear version the kernel K-means algorithm. The results showed that none of the validity indices is superior to the others; in the other hand, the kernel k-means failed to improve clustering accuracy of the dataset from the number of clusters perspective.
It is imperative to analyze educational data especially as it relates to students’ performance. Educational institutions need to have a fairly accurate knowledge of admitted students’ prior academic ability to predict their future academic performance. This helps to identify the good students and also provides an opportunity to pay attention to and improve those who would possibly not perform too well. As a solution, this paper proposed a system which can predict the performance of students from their previous academic record using concepts of data mining techniques under Classification. The dataset contains information about students, such as gender, age, SSCE grade, UTME score, post UTME score and grade in students first year. ID3 (Iterative Dichotomiser 3) and C4.5 classification algorithms was applied on the data to predict the academic performance of students in future examinations.
In this research, the formation of second derivative two-step block hybrid Enright’s linear multistep methods for solving initial value problems is studied. In forming the method, we follow Enright’s 1974 approach, by introducing the off-mesh points at both interpolation and collocations; we developed the continuous schemes for new Enright’s method. The analysis of new Enright method was studied and it was found to be consistent, convergent and zero-stable. We further computed the order, error constants and plotted the region of absolute stability within which the method is A-stable. The methods exhibited better accuracy level when provided with numerical examples than the existing method with which we compared our results.