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The Frechet Reliability for (2+2) Cascade Model 2+2 级联模型的弗雷谢特可靠性
African Journal of Mathematics and Statistics Studies Pub Date : 2024-02-02 DOI: 10.52589/ajmss-fqvgfoiy
Ahmed H. Khaleel
{"title":"The Frechet Reliability for (2+2) Cascade Model","authors":"Ahmed H. Khaleel","doi":"10.52589/ajmss-fqvgfoiy","DOIUrl":"https://doi.org/10.52589/ajmss-fqvgfoiy","url":null,"abstract":"In this paper, a reliability function for one of the cascade models was found; the model consists of two basic components (B_1 and B_2 ) and two spare components (B_3 and B_4 ), and it is sufficient for the model to be in a working state with the presence of two active components and, in case of failure of one of the two basic components, it is compensated with one of the two standby components to keep the model running. It was assumed that the strength-stress factors traced the Frechet, the parameters of the Frechet were estimated by three different estimation methods (Moments, Least Squares and Weighted Least Square,), after which the reliability of the model was estimated. Monte Carlo simulations were also conducted to compare the results and find out which estimation methods are the best to estimate the reliability of the model using two statistical criteria: MSE and MAPE, where it was presented that least square estimation is the preferred for estimating the function of reliability.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"50 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139808973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vibration of Non-Uniform Bernoulli-Euler Beam Under Moving Distributed Masses Resting on Pasternak Elastic Foundation Subjected to Variable Magnitude 位于帕斯捷尔纳克弹性地基上的非均匀伯努利-欧拉梁在移动的分布质量作用下的振动，受不同振幅的影响
African Journal of Mathematics and Statistics Studies Pub Date : 2024-01-07 DOI: 10.52589/ajmss-zqckba87
T. Awodola, B. B. Awe, S. Jimoh
{"title":"Vibration of Non-Uniform Bernoulli-Euler Beam Under Moving Distributed Masses Resting on Pasternak Elastic Foundation Subjected to Variable Magnitude","authors":"T. Awodola, B. B. Awe, S. Jimoh","doi":"10.52589/ajmss-zqckba87","DOIUrl":"https://doi.org/10.52589/ajmss-zqckba87","url":null,"abstract":"This paper investigates the dynamic response of a clamped-clamped non-uniform Bernoulli-Euler beam resting on a Pasternak elastic foundation to variable magnitude moving distributed masses. The predicament is dictated by a partial differential equation of fourth order, which features coefficients that are both variable and singular. The primary aim is to derive an analytical solution for this category of a dynamic problem. To achieve this, we employ the method of Galerkin with a series representation of the Heaviside function to reduce the equation to second-order ordinary differential equations with variable coefficients. We simplify these transformed equations using (i) the Laplace transformation technique in conjunction with convolution theory for solving moving force problems, and (ii) finite element analysis in conjunction with the Newmark method for solving analytically unsolvable moving mass problems due to their harmonic nature. We first solve the moving force problem using the finite element method and compare it against analytical solutions as validation for its accuracy in solving analytically unsolvable moving mass problems. The numerical solution obtained from the finite element method is shown to be comparable favorably against analytical solutions of our moving force problem. Lastly, we calculate displacement response curves for both moving distributed force and mass models at various time t for our dynamical problem presentation purposes.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"9 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139448363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Optimized Single-Step Block Hybrid Nyström-Type Method for Solving Second Order Initial Value Problems of Bratu-Type 解决布拉图式二阶初值问题的优化单步分块混合涅斯特罗姆式方法
African Journal of Mathematics and Statistics Studies Pub Date : 2023-12-12 DOI: 10.52589/ajmss-ednc4fya
Ajinuhi J.O., Mohammed U., Enagi A.I., Jimoh O.R.
{"title":"An Optimized Single-Step Block Hybrid Nyström-Type Method for Solving Second Order Initial Value Problems of Bratu-Type","authors":"Ajinuhi J.O., Mohammed U., Enagi A.I., Jimoh O.R.","doi":"10.52589/ajmss-ednc4fya","DOIUrl":"https://doi.org/10.52589/ajmss-ednc4fya","url":null,"abstract":"In this paper, a global single-step implicit block hybrid Nyström-type method (BHNTM) for solving nonlinear second-order initial-boundary value problems of Bratu-type is developed. The mathematical derivation of the proposed BHNTM is based on the interpolation and multistep collocation techniques with power series polynomials as the trial function. Unlike previous approaches, BHNTM is applied without linearization or restrictive assumptions. The basic properties of the proposed method, such as zero stability, consistency and convergence are analysed. The numerical results from three test problems demonstrate its superiority over existing methods which emphasize the effectiveness and reliability in numerical simulations. Furthermore, as the step size decreases as seen in the test problems, the error drastically reduces, indicating BHNTM's precision. These findings underscore BHNTM's significance in numerical methods for solving differential equations, offering a more precise and dependable approach for addressing complex problems.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"21 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Theory and Application of Two (2) Iterative Imputation Approaches to Nigeria Annual Rainfall Data Reported 尼日利亚年降雨量报告的两(2)种迭代推算方法的理论与应用
African Journal of Mathematics and Statistics Studies Pub Date : 2023-08-24 DOI: 10.52589/ajmss-vdc3azvn
Ogbeide E.M., Shuaibu M., Siloko U.I.
{"title":"Theory and Application of Two (2) Iterative Imputation Approaches to Nigeria Annual Rainfall Data Reported","authors":"Ogbeide E.M., Shuaibu M., Siloko U.I.","doi":"10.52589/ajmss-vdc3azvn","DOIUrl":"https://doi.org/10.52589/ajmss-vdc3azvn","url":null,"abstract":"This research work is based on missing data statistics. Missing data occur where one or more of the observations in a dataset are completely not available. This work focuses on two (2) iterative imputation approaches. These are the Regression approach and the Expectation Maximization iterative imputation. These approaches were used to analyze the secondary data of the thirty-six (36) states in Nigeria on the rainfall data collected from the Annual Abstract of Statistics 2016. The evaluation criteria and comparison of these two approaches were done based on the error efficiency using the Raw Bias (RB), Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and variance. The analysis of the result showed that the Expectation Maximization (EM) method was better for this specific data as reported in the Annual Abstract of Statistics 2016, compared to the other approaches. This was seen in the smaller errors values from the computed cases. It is therefore recommended that this approach should be used for obtaining missing data like other rainfall data in Nigeria. These two imputation approaches are good for making available missing data in observations.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"37 45","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113934282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximating Linear Programming by Geometric Programming and Its Application to Urban Planning 用几何规划逼近线性规划及其在城市规划中的应用
African Journal of Mathematics and Statistics Studies Pub Date : 2023-08-14 DOI: 10.52589/ajmss-rx6k6m0k
Harrison O.A., Christy C.N., Bridget N.O., Immaculata O.O., Sylvester A.I.
{"title":"Approximating Linear Programming by Geometric Programming and Its Application to Urban Planning","authors":"Harrison O.A., Christy C.N., Bridget N.O., Immaculata O.O., Sylvester A.I.","doi":"10.52589/ajmss-rx6k6m0k","DOIUrl":"https://doi.org/10.52589/ajmss-rx6k6m0k","url":null,"abstract":"In this study, we approximated linear programming by geometric programming; the developed method converts linear programming to geometric programming. We applied the developed method to Neighbourhood planning, a vital aspect of urban planning, and obtained the optimal cost of Neighbourhood designs. The method demonstrated that geometric programming is a robust non-linear optimization model that can be extended to approximate linear optimization problems. This method has obvious advantages in the sense that it allows every decision variable to contribute to the optimal objective function. This is not the case with the known regular Simplex method and the Interior Point Algorithm of solution to linear programming which assign zeros to some variables when the matrix of the non-basic variables is rectangular or when some of the non-basic variables did not enter the basis. The developed method was used to find the global optimal solution, optimal primal and dual decision variables. The solution was better compared to the linear programming method via Simplex method or Interior Point Algorithm because it achieved the global optimal solution. We observed that in addition to achieving the global optimal solution, we obtained the optimal dual decision variables which was absent in the other methods and all the primal decision variables have value against the other methods that assigned some of the variables with zeroes.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127851642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Prognosis Method on the Outcome of Covid-19 Patients in Senegal 塞内加尔新冠肺炎患者预后的预测方法
African Journal of Mathematics and Statistics Studies Pub Date : 2023-08-01 DOI: 10.52589/ajmss-vgaf69po
Seck C.T., Faye I., D. A., Niang M.A., Sylla S.N., Ndao A., Idrissa S.
{"title":"Prognosis Method on the Outcome of Covid-19 Patients in Senegal","authors":"Seck C.T., Faye I., D. A., Niang M.A., Sylla S.N., Ndao A., Idrissa S.","doi":"10.52589/ajmss-vgaf69po","DOIUrl":"https://doi.org/10.52589/ajmss-vgaf69po","url":null,"abstract":"There have been disturbing waves of Covid-19 deaths in many countries due to a lack of adequate treatment in the early stages of the pandemic but also to the presence of co-morbidities in many hospitalised patients. This work aims to determine the discriminatory features between the surviving patients and the deceased ones after their hospitalisation to propose a new method of prognosis on the outcome of a new patient under treatment. To this end, we use three supervised classification methods, each allowing us to select the most significant features associated with patient death. These are binary logistic regression (BLR), random forests (RF), and support vector machines (SVM). The data comes from the Ministry of Health and Social Action of Senegal and covers the period from March 2020 to December 2022. Age emerged as the most discriminatory factor between the two patient groups: survivors and deceased. The study found that patients 60 and older are more likely to die of Covid-19.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129131047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Typology of Health Districts Based on Data from Ten Infectious Diseases Under Surveillance in Senegal 基于塞内加尔10种传染病监测数据的卫生区类型研究
African Journal of Mathematics and Statistics Studies Pub Date : 2023-08-01 DOI: 10.52589/ajmss-aonooefg
Abdourahmane N., Cheikh T.S.
{"title":"Typology of Health Districts Based on Data from Ten Infectious Diseases Under Surveillance in Senegal","authors":"Abdourahmane N., Cheikh T.S.","doi":"10.52589/ajmss-aonooefg","DOIUrl":"https://doi.org/10.52589/ajmss-aonooefg","url":null,"abstract":"The aim of this work is to construct a typology of health districts in Senegal based on the distribution frequency of ten infectious diseases under surveillance. Our methodology utilizes HCPC (Hierarchical Classification on Principal Components) algorithm which combines two data analysis techniques, namely Principal Component Analysis (PCA) and Hierarchical Ascending Classification (HAC). The data come from the Prevention Department of the Ministry of Health and Social Action and cover the period from January 2018 to November 2022. The results show that health districts in Senegal can be divided into three clusters according to the number of confirmed cases recorded for each of the ten considered infectious diseases. Moreover, the parangons’ principle allows us to select from the obtained clusters a representative stratified sample of health districts in view to identifying risk factors associated with these ten pathologies.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121962776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calculation of a Class of Confluent Hypergeometric Equation and Analysis of its Roles in Option Pricing Models 一类合流超几何方程的计算及其在期权定价模型中的作用分析
African Journal of Mathematics and Statistics Studies Pub Date : 2023-07-21 DOI: 10.52589/ajmss-zxrd77uv
J. I. Adindu-Dick
{"title":"Calculation of a Class of Confluent Hypergeometric Equation and Analysis of its Roles in Option Pricing Models","authors":"J. I. Adindu-Dick","doi":"10.52589/ajmss-zxrd77uv","DOIUrl":"https://doi.org/10.52589/ajmss-zxrd77uv","url":null,"abstract":"The confluent hypergeometric equation is one of the most important differential equations in physics, chemistry, finance and many more. This work deals with the power series solution of a class of confluent hypergeometric equation with α, a real constant and z, an independent variable. The confluent hypergeometric function of the first kind M(α,α+2,z) is derived together with the second power series solution, M ̃(α,α+2,z). The analysis of the roles of the derived function in option pricing models are given.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128531959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparison of Adomian Decomposition Method with Differential Transformation Method for Unsteady MHD Flow and Heat Transfer Over a Stretching/Shrinking Permeable Sheet with Ohmic Heating Adomian分解法与微分变换法在欧姆加热拉伸/收缩渗透片上非定常流动与传热的比较
African Journal of Mathematics and Statistics Studies Pub Date : 2023-07-12 DOI: 10.52589/ajmss-nuacwt1m
Ebiwareme L., B. K.W., Davies O.A.
{"title":"Comparison of Adomian Decomposition Method with Differential Transformation Method for Unsteady MHD Flow and Heat Transfer Over a Stretching/Shrinking Permeable Sheet with Ohmic Heating","authors":"Ebiwareme L., B. K.W., Davies O.A.","doi":"10.52589/ajmss-nuacwt1m","DOIUrl":"https://doi.org/10.52589/ajmss-nuacwt1m","url":null,"abstract":"In this paper, two semi-analytical techniques were implemented to solve a two-dimensional unsteady MHD fluid flow and heat transfer through a stretching/shrinking permeable sheet with ohmic heating and viscous dissipation. The governing flow equations in PDE form were reduced to ordinary differential equations using appropriate similarity transformation. We obtained approximate expressions for the velocity and temperature profiles. Comparative results obtained employing Adomian decomposition method and differential transformation method were benchmarked against a numerical solution using Keller box scheme. Our findings revealed that the approximate analytical solution obtained using DTM is more dependable with fast convergence, highly accurate with minimal calculations and computationally convenient. However, the requirement of Adomian polynomials to tackle the nonlinear terms in ADM makes its execution sometimes cumbersome and difficult.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128323445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Review of Some Robust Estimators in Multiple Linear Regressions in the Presence of Outlier(s) 存在离群值的多元线性回归中若干鲁棒估计的综述
African Journal of Mathematics and Statistics Studies Pub Date : 2023-06-26 DOI: 10.52589/ajmss-ec8ewxul
A. T., Oyeyemi G.M., Olaniran R.O., Adetunji K.O.
{"title":"Review of Some Robust Estimators in Multiple Linear Regressions in the Presence of Outlier(s)","authors":"A. T., Oyeyemi G.M., Olaniran R.O., Adetunji K.O.","doi":"10.52589/ajmss-ec8ewxul","DOIUrl":"https://doi.org/10.52589/ajmss-ec8ewxul","url":null,"abstract":"Linear regression has been one of the most important statistical data analysis tools. Multiple regression is a type of regression where the dependent variable shows a linear relationship with two or more independent variables. OLS estimate is extremely sensitive to unusual observations (outliers), with low breakdown point and low efficiency. This paper reviews and compares some of the existing robust methods (Least Absolute Deviation, Huber M-Estimator, Bisquare M-Estimator, MM Estimator, Least Median Square, Least Trimmed Square, S-Estimator); a simulation method is used to compare the selected existing methods. It was concluded based on the results that for y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.3 is MM; for x direction outlier, the best estimator in term breakdown point of at most 0.4 is S; for x, y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.2 is MM.","PeriodicalId":251990,"journal":{"name":"African Journal of Mathematics and Statistics Studies","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127380762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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