Journal of Mathematics and Statistics Studies

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EISSN : 2709-4200
Total articles ≅ 9
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, Madjda Amrani
Journal of Mathematics and Statistics Studies, Volume 2, pp 01-07; doi:10.32996/jmss.2021.2.2.1

Abstract:
In this work, we study the famous model of volatility; called model of conditional heteroscedastic autoregressive with mixed memory MMGARCH for modeling nonlinear time series. The MMGARCH model has two mixing components, one is a GARCH short memory and the other is GARCH long memory. the main objective of this search for finds the best model between mixtures of the models we made (long memory with long memory, short memory with short memory and short memory with long memory) Also, the existence of its stationary solution is discussed. The Monte Carlo experiments demonstrate we discovered theoretical. In addition, the empirical application of the MMGARCH model (1, 1) to the daily index DOW and NASDAQ illustrates its capabilities; we find that for the mixture between APARCH and EGARCH is superior to any other model tested because it produces the smallest errors.
Olalude Gbenga Adelekan, , Amusan Ajitoni Simeon
Journal of Mathematics and Statistics Studies, Volume 2, pp 53-61; doi:10.32996/jmss.2021.2.1.6

Abstract:
The study introduced a special case of the Poisson-Generalized Gamma empirical Bayes model to survey states in Nigeria with a higher risk of fatal accidents. Monte Carlo error and stationary dynamic trace plots were used to validate model convergence and accuracy of the posterior estimates. The main results included the disease mappings that revealed Ebonyi had the highest risk of road vehicular fatal accidents in Nigeria with a relative risk estimate of 1.4120 while Abuja had the lowest risk with a relative risk estimate 0.5711. In terms of geopolitical region, the risk of road vehicular fatal accident is highest in South-South region with a relative risk estimate of 1.1850 while North-Central had the lowest risk with a relative risk estimate of 0.7846. The study is to aid planned government programs to ameliorate vehicular road carnage in Nigeria.
, Ugochinyere Ihuoma Nwosu, Desmond Chekwube Bartholomew
Journal of Mathematics and Statistics Studies, Volume 2, pp 40-52; doi:10.32996/jmss.2021.2.1.5

Abstract:
This study modeled the US Dollar and Nigerian Naira exchange rates during COVID-19 pandemic period using a classical statistical method – Autoregressive Integrated Moving Average (ARIMA) – and two machine learning methods – Artificial Neural Network (ANN) and Random Forest (RF). The data were divided into two sets namely: the training set and the test set. The training set was used to obtain the parameters of the model, and the performance of the estimated model was validated on the test set that served as new data. Though the ARIMA and random forest performed slightly better than the neural network in the training set, their performance in the test set was poor. The neural network with 5 nodes in the input layer, 5 nodes in the hidden layer and 1 node in the output layer (ANN (5,5,1)) performed better on the new data set (test set) and is chosen as the best model to forecast for future USD to NGN exchange rate. The information from the high-performance model (ANN (5, 5, 1)) for modeling the USD to NGN exchange rate will assist econometric trading of the currencies and offer both speculative and precautionary assistance to individuals, households, firms and nations who use the currencies locally and for international trade.
, Chukwunenye Ukwu
Journal of Mathematics and Statistics Studies, Volume 2, pp 62-87; doi:10.32996/jmss.2021.2.1.7

Abstract:
Three major tools are required to investigate the controllability of control systems, namely, determining matrices, index of control systems and controllability Grammian. Determining matrices are the preferred choice for autonomous control systems due to the fact that they are devoid of integral operators in their computations. This article developed the structure of certain parameter-ordered determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for Euclidean controllability of the system. Expressions for the relevant determining matrices were formulated and it was established that the determining matrices for double time-delay linear autonomous functional differential control systems do not exist if one of the time-delays is not an integer multiple of the other paving the way for the investigation of the Euclidean controllability of generic double time-delay control systems.
Chukwunenye Ukwu,
Journal of Mathematics and Statistics Studies, Volume 2, pp 88-101; doi:10.32996/jmss.2021.2.1.8

Abstract:
This paper developed and established unprecedented global results on the structure of determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for the Euclidean controllability of the system. The computational process and implementation of the controllability matrix were demonstrated on the MATLAB platform to determine the controllability disposition of a small-problem instance. Finally, the work examined the computing complexity of the determining matrices.
Urvisha Vaghela, Dharamvirsinh Parmar
Journal of Mathematics and Statistics Studies, Volume 2, pp 26-39; doi:10.32996/jmss.2021.2.1.4

Abstract:
Let graph G=(V(G),E(G)) attains a Skolem difference mean labeling with p vertices and q edges is said to be an extra Skolem difference mean labeling of graph G if all the labels of the vertices are odd. The graph which attains an extra Skolem difference mean labeling is called an extra Skolem difference mean graph. We obtain an extra Skolem difference mean labeling for Comb graph, Twig of a path P_n, H graph of a path P_n, K_1,2*K_(1,n) graph, K_1,3*K_(1,n) graph, m- Join of H_n, P_n⊙K_(1,m) graph , HSS(P_n) graph, H⊙〖mK〗_1-graph of a path P_n.
, Mariel Africa, Mary-Ann Guilleno, Anne Jeannette C. Pamplona, Jennifer Torrefranca, Levi E. Elipane
Journal of Mathematics and Statistics Studies, Volume 2, pp 21-25; doi:10.32996/jmss.2021.2.1.3

Abstract:
This paper explores Van Hiele’s Model's use in planning the tasks to identify the properties of quadrilaterals. Lesson study, a professional development program that enables teachers to collaborate to improve teaching and learning quality, was utilized to get necessary data needed for the study. The authors aimed to see to what extent Van Hiele’s Model affects the students’ engagement and development of knowledge in the learning of the research topic. Some observations during the research lesson were as follows: 1) retention of prior knowledge on quadrilaterals was little to non-evident to the students 2) most students still use jargons in order to describe the properties of quadrilaterals and 3) most students were not able to showcase skills in measuring lengths and angles in identifying properties of the quadrilaterals. Given these observations, the following recommendations were as follows: 1) continuous integration and use of mathematical tools such as ruler and protractor in teaching different concepts and processes in Mathematics 2) identifying the level of the learners’ readiness based on the Van Hiele’s model to provide appropriate examples and activities in the context of the students 3) providing hands-on activities such as geometric construction and measuring activities that would enhance students’ capabilities in reasoning and proving. Lesson study served as a powerful tool to reflect on the researchers' processes and activities in conducting the study.
Olusegun O. Alabi Kayode Ayinde,
Journal of Mathematics and Statistics Studies, Volume 2, pp 12-20; doi:10.32996/jmss.2021.2.1.2

Abstract:
Multicollinearity has remained a major problem in regression analysis and should be sustainably addressed. Problems associated with multicollinearity are worse when it occurs at high level among regressors. This review revealed that studies on the subject have focused on developing estimators regardless of effect of differences in levels of multicollinearity among regressors. Studies have considered single-estimator and combined-estimator approaches without sustainable solution to multicollinearity problems. The possible influence of partitioning the regressors according to multicollinearity levels and extracting from each group to develop estimators that will estimate the parameters of a linear regression model when multicollinearity occurs is a new econometrics idea and therefore requires attention. The results of new studies should be compared with existing methods namely principal components estimator, partial least squares estimator, ridge regression estimator and the ordinary least square estimators using wide range of criteria by ranking their performances at each level of multicollinearity parameter and sample size. Based on a recent clue in literature, it is possible to develop innovative estimator that will sustainably solve the problem of multicollinearity through partitioning and extraction of explanatory variables approaches and identify situations where the innovative estimator will produce most efficient result of the model parameters. The new estimator should be applied to real data and popularized for use.
Ahmed Nafidi, , Boujemaa Achchab
Journal of Mathematics and Statistics Studies, Volume 2, pp 01-11; doi:10.32996/jmss.2021.2.1.1

Abstract:
A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.
Journal of Mathematics and Statistics Studies, Volume 1, pp 26-37; doi:10.32996/ijllt.2020.1.2.3

Abstract:
Shaped with Vygotsky’s Principle on Scaffolding, this study aimed to develop and validate learning materials known as Strategic Intervention Materials (SIMs) of the selected topics in Trigonometry in the STEM strand. This developmental study undertook three phases, namely: planning, development, and validation and guided by the ADDIE Model in the data analysis. In the planning stage, the least-mastered competencies (LMC) were selected based on the results of their final examination in Pre-Calculus in the field of Trigonometry. The researcher made two SIMs based on the identified (LMC). The second stage is the development of the materials that were presented and critiqued by the thesis adviser, students, colleagues, and SIM experts. In the last stage, the content and student validators validated the developed learning materials. The validators were purposively chosen. The adapted instrument was used in validating the materials. The developed SIMs were rated “excellent” by the content-validators and “more than adequate” by the student-validators. This implied that the content-validators considered the SIMs as teacher support materials that can be used to master the competencies in Pre-Calculus and learner enhancers to improve their competence as evaluated by the student-validators. The validation results of the two SIMs paved the way for the construction of the new learning material to confirm the findings and undergone validation were rated “excellent” and “more than adequate” by content and student validators respectively. It is recommended that teachers should develop more SIMs for other disciplines to address students’ difficulties in learning Trigonometry.
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