Numerical solution of ordinary differential equations is the most important technique which is widely used for mathematical modelling in science and engineering. The differential equation that describes the problem is typically too complex to precisely solve in real-world circumstances. Since most ordinary differential equations are not solvable analytically, numerical computations are the only way to obtain information about the solution. Many different methods have been proposed and used is an attempt to solve accurately various types of ordinary differential equations. Among them, Runge-Kutta is a well-known and popular method because of their good efficiency. This paper contains an analysis for the computations of the modified Runge-Kutta method for nonlinear second order initial value problems. This method is wide quite efficient and practically well suited for solving linear and non-linear problems. In order to verify the accuracy, we compare numerical solution with the exact solution. We also compare the performance and the computational effort of this method. In order to achieve higher accuracy in the solution, the step size needs to be small. Finally, we take some examples of non-linear initial value problems (IVPs) to verify proposed method. The results of that example indicate that the convergence, stability analysis, and error analysis which are discussed to determine the efficiency of the method.
{"title":"NUMERICAL COMPUTATIONS OF GENERAL NON-LINEAR SECOND ORDER INITIAL VALUE PROBLEMS BY USING MODIFIED RUNGE-KUTTA METHOD","authors":"Nazrul Islam, Md. Shorif Hossan, Md. Parvez Mosharaf, Md. Rayhan Prodhan","doi":"10.26480/msmk.02.2022.34.40","DOIUrl":"https://doi.org/10.26480/msmk.02.2022.34.40","url":null,"abstract":"Numerical solution of ordinary differential equations is the most important technique which is widely used for mathematical modelling in science and engineering. The differential equation that describes the problem is typically too complex to precisely solve in real-world circumstances. Since most ordinary differential equations are not solvable analytically, numerical computations are the only way to obtain information about the solution. Many different methods have been proposed and used is an attempt to solve accurately various types of ordinary differential equations. Among them, Runge-Kutta is a well-known and popular method because of their good efficiency. This paper contains an analysis for the computations of the modified Runge-Kutta method for nonlinear second order initial value problems. This method is wide quite efficient and practically well suited for solving linear and non-linear problems. In order to verify the accuracy, we compare numerical solution with the exact solution. We also compare the performance and the computational effort of this method. In order to achieve higher accuracy in the solution, the step size needs to be small. Finally, we take some examples of non-linear initial value problems (IVPs) to verify proposed method. The results of that example indicate that the convergence, stability analysis, and error analysis which are discussed to determine the efficiency of the method.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69337125","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.02.2022.58.63
R. De, Ipseeta Nanda
Electromagnetic Radiation comes out from different electrical, or electronics gadget used for Lab as well as household purposes. As many circuits of household, industrial, and communication systems operate at close proximity of each other and one such circuit can affect the performance of other nearby circuits adversely via inadvertent couplings of their signal through near and far region, propagating electromagnetic fields. Electromagnetic waves generated by different wireless systems like mobile systems, satellite systems, other microwave links, etc. facilitates our communications throughout the world. Thus the hazard of electromagnetic radiation causes interference among these instruments and at the same time affects the living cells which includes both plant and animal cells. Here our research is to study the electromagnetic radiation of all these instruments including mobile phones on the plant cells. For the purpose of this study, here Hibiscus Flower is taken, exposed to electromagnetic radiation for the different time interval with a constant power and at certain temperature. It is observed that the physical condition of the flower as well as dielectric constants is changed. Here, in this case the dielectric properties have been measured on a flower named Hibiscus (petals) using open ended coaxial probe technique at four different temperature levels i.e. at 0th hour, after 1hour, after 2hours and after 3 hours. There are the dielectrics properties for mentioned flowers have been measured and plotted graphically within frequency range of 0.02 GHz to 8.5 GHz at many sample points. Another important observation is that the condition of Hibiscus petals at different time interval after exposing electronic magnetic radiation from Horn Antenna. From this study we can get an idea that how electromagnetic radiation can be affected for plants.
{"title":"STUDY OF ELECTROMAGNETIC RADIATION ON FLOWER","authors":"R. De, Ipseeta Nanda","doi":"10.26480/msmk.02.2022.58.63","DOIUrl":"https://doi.org/10.26480/msmk.02.2022.58.63","url":null,"abstract":"Electromagnetic Radiation comes out from different electrical, or electronics gadget used for Lab as well as household purposes. As many circuits of household, industrial, and communication systems operate at close proximity of each other and one such circuit can affect the performance of other nearby circuits adversely via inadvertent couplings of their signal through near and far region, propagating electromagnetic fields. Electromagnetic waves generated by different wireless systems like mobile systems, satellite systems, other microwave links, etc. facilitates our communications throughout the world. Thus the hazard of electromagnetic radiation causes interference among these instruments and at the same time affects the living cells which includes both plant and animal cells. Here our research is to study the electromagnetic radiation of all these instruments including mobile phones on the plant cells. For the purpose of this study, here Hibiscus Flower is taken, exposed to electromagnetic radiation for the different time interval with a constant power and at certain temperature. It is observed that the physical condition of the flower as well as dielectric constants is changed. Here, in this case the dielectric properties have been measured on a flower named Hibiscus (petals) using open ended coaxial probe technique at four different temperature levels i.e. at 0th hour, after 1hour, after 2hours and after 3 hours. There are the dielectrics properties for mentioned flowers have been measured and plotted graphically within frequency range of 0.02 GHz to 8.5 GHz at many sample points. Another important observation is that the condition of Hibiscus petals at different time interval after exposing electronic magnetic radiation from Horn Antenna. From this study we can get an idea that how electromagnetic radiation can be affected for plants.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69337215","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.01.2022.05.12
D. Akpootu, M. Iliyasu, B. Olomiyesan, S. Fagbemi, S. B. Sharafa, M. Idris, Z. Abdullahi, N. O. Meseke
This study developed two to six multivariate regression equations that reliably predict global radiation in Jos (Latitude 9.87 °𝑁 and Longitude 8.75 °𝐸). Thirty-one years (1980 – 2010) observed monthly mean daily global solar radiation, sunshine hours, maximum and minimum temperatures, cloud cover, rainfall, relative humidity and wind speed data were used in this study with the clearness index as the response variable and other variables as predictors. The seven validation indices employed are the coefficient of determination (R2), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t – test, Nash – Sutcliffe Equation (NSE) and Index of Agreement (IA) to determine the reliability, suitability and applicability of the developed models. The results in this study revealed that all the developed multivariate models were found reliable for global solar radiation estimation in Jos depending on the obtainable meteorological data measured in the location. The correlation between the measured and predicted (developed) global solar radiation shows a perfect correlation as depicted from the figures.
{"title":"MULTIVARIATE MODELS FOR PREDICTING GLOBAL SOLAR RADIATION IN JOS, NIGERIA","authors":"D. Akpootu, M. Iliyasu, B. Olomiyesan, S. Fagbemi, S. B. Sharafa, M. Idris, Z. Abdullahi, N. O. Meseke","doi":"10.26480/msmk.01.2022.05.12","DOIUrl":"https://doi.org/10.26480/msmk.01.2022.05.12","url":null,"abstract":"This study developed two to six multivariate regression equations that reliably predict global radiation in Jos (Latitude 9.87 °𝑁 and Longitude 8.75 °𝐸). Thirty-one years (1980 – 2010) observed monthly mean daily global solar radiation, sunshine hours, maximum and minimum temperatures, cloud cover, rainfall, relative humidity and wind speed data were used in this study with the clearness index as the response variable and other variables as predictors. The seven validation indices employed are the coefficient of determination (R2), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t – test, Nash – Sutcliffe Equation (NSE) and Index of Agreement (IA) to determine the reliability, suitability and applicability of the developed models. The results in this study revealed that all the developed multivariate models were found reliable for global solar radiation estimation in Jos depending on the obtainable meteorological data measured in the location. The correlation between the measured and predicted (developed) global solar radiation shows a perfect correlation as depicted from the figures.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336518","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.01.2022.13.20
M. Deiaa, W. S. Elbeshbeeshy, I. El-Kalla, A. Elsaid
In this article, we construct an approximate series solution for the one-dimensional one-phase Stefan-like problems with a forcing term. An algorithm is proposed to represent the nonhomogeneous forcing term in a moving series form to incorporate it into the moving Taylor series method. Numerical examples are solved by the proposed algorithm and the results show that with a suitable number of terms in the utilized moving series, the approximate solution is in good agreement with the exact solution.
{"title":"THE SOLUTION OF ONE-PHASE STEFAN-LIKE PROBLEMS WITH A FORCING TERM BY MOVING TAYLOR SERIES","authors":"M. Deiaa, W. S. Elbeshbeeshy, I. El-Kalla, A. Elsaid","doi":"10.26480/msmk.01.2022.13.20","DOIUrl":"https://doi.org/10.26480/msmk.01.2022.13.20","url":null,"abstract":"In this article, we construct an approximate series solution for the one-dimensional one-phase Stefan-like problems with a forcing term. An algorithm is proposed to represent the nonhomogeneous forcing term in a moving series form to incorporate it into the moving Taylor series method. Numerical examples are solved by the proposed algorithm and the results show that with a suitable number of terms in the utilized moving series, the approximate solution is in good agreement with the exact solution.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336563","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.02.2022.30.33
Bawar Mohammed Faraj, Shnyar Karim Rahman, Deni Adnan Mohammed, Bahadin Muhammad Hussein, Berivan Azad Salam, Khadijah Mohammed
In the present study numerical solution for non linear equations have been studied. Ridders methodd have been discussed. An improvement of Ridders method with combination of Bisection and newton Raphson methods have been presented. An algorithm for the proposed method have been stated. Moreover, several examples are included to demonstrate the validity and applicability of the presented technique. Matlab program involved for numerical computations. The proposed method applied for given examples. The error analysis table presents the obtained numerical results. The numerical solutions which found by Matlab program has good results in terms of accuracy.
{"title":"AN IMPROVED BRACKETING METHOD FOR NUMERICAL SOLUTION OF NONLINEAR EQUATIONS BASED ON RIDDERS METHOD","authors":"Bawar Mohammed Faraj, Shnyar Karim Rahman, Deni Adnan Mohammed, Bahadin Muhammad Hussein, Berivan Azad Salam, Khadijah Mohammed","doi":"10.26480/msmk.02.2022.30.33","DOIUrl":"https://doi.org/10.26480/msmk.02.2022.30.33","url":null,"abstract":"In the present study numerical solution for non linear equations have been studied. Ridders methodd have been discussed. An improvement of Ridders method with combination of Bisection and newton Raphson methods have been presented. An algorithm for the proposed method have been stated. Moreover, several examples are included to demonstrate the validity and applicability of the presented technique. Matlab program involved for numerical computations. The proposed method applied for given examples. The error analysis table presents the obtained numerical results. The numerical solutions which found by Matlab program has good results in terms of accuracy.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336653","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.01.2022.21.25
Deniz Elmaci, Nurcan Baykus, Savasaneril .
In this study, linear Volterra-Fredholm integral equations are approximatively solved in terms of Lucas polynomials about any point in this study using a practical matrix approach. This technique uses collocation points and Lucas polynomials to transform the aforementioned linear Volterra-Fredholm integral problem into a matrix equation. Lucas coefficients are unknown in the system of linear algebraic equations. With the use of an error estimation, some illustrated examples are also provided. The outcomes demonstrate how effective and practical the suggested methodology is. Code was created in MATLAB to acquire the matrix equations and answers for the chosen issues.
{"title":"THE LUCAS POLYNOMIAL SOLUTION OF LINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS","authors":"Deniz Elmaci, Nurcan Baykus, Savasaneril .","doi":"10.26480/msmk.01.2022.21.25","DOIUrl":"https://doi.org/10.26480/msmk.01.2022.21.25","url":null,"abstract":"In this study, linear Volterra-Fredholm integral equations are approximatively solved in terms of Lucas polynomials about any point in this study using a practical matrix approach. This technique uses collocation points and Lucas polynomials to transform the aforementioned linear Volterra-Fredholm integral problem into a matrix equation. Lucas coefficients are unknown in the system of linear algebraic equations. With the use of an error estimation, some illustrated examples are also provided. The outcomes demonstrate how effective and practical the suggested methodology is. Code was created in MATLAB to acquire the matrix equations and answers for the chosen issues.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336569","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.02.2022.52.57
R. De, Ipseeta Nanda, Varsha Kumari
Cloud computing is a platform for dynamically enhancing capabilities and increasing potentialities without requiring the addition of new hardware, employees, or software. Additionally, cloud computing began as a business notion and later became a successful IT innovation. Concerns have been expressed about the security of the cloud environment, though, considering that the cloud contains a lot of information about people and businesses. Although cloud computing has received a lot of attention, clients are still hesitant to move their businesses there. However, the only significant issue preventing greater adoption of cloud computing is a lack of protection. Additionally, the market is wary about cloud computing due to the intricacy with which it controls data protection and confidentiality. When used in a cloud context, the cloud model architecture jeopardises the security of current technology. Therefore, cloud service customers should be aware of the risks associated with uploading data into this novel environment. Therefore, several areas of cryptography that endanger cloud computing are examined in this work. This paper provides an overview of the specific security concerns that using cryptography in a cloud computing system raises.
{"title":"CLOUD COMPUTING’S USE OF CRYPTOGRAPHY","authors":"R. De, Ipseeta Nanda, Varsha Kumari","doi":"10.26480/msmk.02.2022.52.57","DOIUrl":"https://doi.org/10.26480/msmk.02.2022.52.57","url":null,"abstract":"Cloud computing is a platform for dynamically enhancing capabilities and increasing potentialities without requiring the addition of new hardware, employees, or software. Additionally, cloud computing began as a business notion and later became a successful IT innovation. Concerns have been expressed about the security of the cloud environment, though, considering that the cloud contains a lot of information about people and businesses. Although cloud computing has received a lot of attention, clients are still hesitant to move their businesses there. However, the only significant issue preventing greater adoption of cloud computing is a lack of protection. Additionally, the market is wary about cloud computing due to the intricacy with which it controls data protection and confidentiality. When used in a cloud context, the cloud model architecture jeopardises the security of current technology. Therefore, cloud service customers should be aware of the risks associated with uploading data into this novel environment. Therefore, several areas of cryptography that endanger cloud computing are examined in this work. This paper provides an overview of the specific security concerns that using cryptography in a cloud computing system raises.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69337162","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}
Linear programming is a mathematical method for choosing the best product combination to maximize profit or decrease cost within the limitations of available resources. In this article, we have proposed the linear programming application for profit Maximization of a Biscuit Factory in Bangladesh. For linear programming problems, the Simplex algorithm provides a powerful computational tool, able to provide fast solution to very large-scale application. The optimization principal examined unit cost of production, the selling price and the quantity of different raw materials used in production. A model for the problem was formulated and optimum results derived using software that employed simplex method. Our main goal is to emphasize the uniqueness of linear programming modeling at the business level as an optimization technique, and to encourage manufacturing companies to employ linear programming to determine their optimal profit.
{"title":"APPLICATION OF LINEAR PROGRAMMING FOR PROFIT MAXIMIZATION: A CASE STUDY OF A COOKIES FACTORY IN BANGLADESH","authors":"Nazrul Islam, Afsana Yeasmin Mim, Md. Rayhan Prodhan","doi":"10.26480/msmk.01.2022.01.04","DOIUrl":"https://doi.org/10.26480/msmk.01.2022.01.04","url":null,"abstract":"Linear programming is a mathematical method for choosing the best product combination to maximize profit or decrease cost within the limitations of available resources. In this article, we have proposed the linear programming application for profit Maximization of a Biscuit Factory in Bangladesh. For linear programming problems, the Simplex algorithm provides a powerful computational tool, able to provide fast solution to very large-scale application. The optimization principal examined unit cost of production, the selling price and the quantity of different raw materials used in production. A model for the problem was formulated and optimum results derived using software that employed simplex method. Our main goal is to emphasize the uniqueness of linear programming modeling at the business level as an optimization technique, and to encourage manufacturing companies to employ linear programming to determine their optimal profit.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336514","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.01.2020.14.19
Kifilideen L. Osanyinpeju
The different methods used in the multiplication of numbers are long method (column method) of multiplication, grid methods and addition methods of multiplication. The utilization of the methods mentioned to solve power (index) of base number (number that multiply itself in a number of times) are horrendous, outrageous, tedious, time consuming and too long to be carried out. This study develops computation of the power of base of number using Kifilideen (matrix, combination and distributive (MCD)) approach. The Kif matrix method of multiplication is a shorter version of the long method (column method) of multiplication. The matrix method provides a straight forward, direct and systematic means of multiplication of digit number that multiply itself repetitively
在数字乘法中使用的不同方法有长法(列法)乘法、网格法乘法和加法乘法。使用上述方法求解底数(自身乘以若干次的数)的幂(指数)是可怕的，令人发指的，繁琐的，耗时的，而且执行起来太长。本文利用Kifilideen (matrix, combination and distribution, MCD)方法发展了数的底数幂的计算。Kif矩阵乘法法是长乘法法(列乘法法)的简化版。矩阵法提供了一种简单、直接和系统的方法来计算重复相乘的数字的乘法
{"title":"COMPUTATION OF THE POWER OF BASE OF TWO DIGITS NUMBER USING KIFILIDEEN (MATRIX, COMBINATION AND DISTRIBUTIVE (MCD)) APPROACH","authors":"Kifilideen L. Osanyinpeju","doi":"10.26480/msmk.01.2020.14.19","DOIUrl":"https://doi.org/10.26480/msmk.01.2020.14.19","url":null,"abstract":"The different methods used in the multiplication of numbers are long method (column method) of multiplication, grid methods and addition methods of multiplication. The utilization of the methods mentioned to solve power (index) of base number (number that multiply itself in a number of times) are horrendous, outrageous, tedious, time consuming and too long to be carried out. This study develops computation of the power of base of number using Kifilideen (matrix, combination and distributive (MCD)) approach. The Kif matrix method of multiplication is a shorter version of the long method (column method) of multiplication. The matrix method provides a straight forward, direct and systematic means of multiplication of digit number that multiply itself repetitively","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336508","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}
Pub Date : 2022-01-01DOI: 10.26480/msmk.01.2022.26.29
Ilugbo Stephen Olubusola, Raji Idowu, O. Adeyanju, Afolabi Habeeb Abiodun
It has been shown that Ranked Set Sampling (RSS) is highly beneficial to the estimation based on Simple Random Sampling (SRS). There has been considerable development and many modifications were done to this method. The problem of estimating the population means is an integral aspect of a scientific survey. The estimators were examined for cum-dual products under Ranked Set Sampling (RSS), while the first-order approximation to the bias and Mean Square Error (MSE) of the proposed estimators were obtained. The numerical illustration of the comparisons was carried out to support the claim that the proposed estimators are more efficient than some existing estimators. Data were simulated for study variable y and auxiliary variable x using R software for the analysis to support the claim. The result shows that MSE of the proposed estimators, y ̅_(pd,RSS)^* is smaller than the MSE of the existing estimators y ̅_pd^*,y ̅_Rd^*, y ̅_(R,RSS)^*,y ̅_(RSS,MM1)^* and y ̅_(RSS,MM2)^* and y ̅_(RSS,MM3)^* at ρ = −0.1,−0.2,0.1,0.2, hence, the proposed estimator performed better than the existing estimators. While the MSE of the proposed estimator yy ̅_(pd,RSS)^* is greater than the MSE of the existing estimators y ̅_pd^* and y ̅_Rd^* at ρ = -0.3 and 0.3. However, the proposed estimator y ̅_(pd,RSS)^* does not perform better than the estimators, y ̅_pd^*,and y ̅_Rd^* at ρ = -0.3 and 0.3. It was concluded that the proposed estimator was more efficient than a class of regression estimators and four existing ratio-type estimators based on RSS.
{"title":"CUM DUAL PRODUCT ESTIMATOR FOR THE POPULATION MEAN USING RANKED SET SAMPLING","authors":"Ilugbo Stephen Olubusola, Raji Idowu, O. Adeyanju, Afolabi Habeeb Abiodun","doi":"10.26480/msmk.01.2022.26.29","DOIUrl":"https://doi.org/10.26480/msmk.01.2022.26.29","url":null,"abstract":"It has been shown that Ranked Set Sampling (RSS) is highly beneficial to the estimation based on Simple Random Sampling (SRS). There has been considerable development and many modifications were done to this method. The problem of estimating the population means is an integral aspect of a scientific survey. The estimators were examined for cum-dual products under Ranked Set Sampling (RSS), while the first-order approximation to the bias and Mean Square Error (MSE) of the proposed estimators were obtained. The numerical illustration of the comparisons was carried out to support the claim that the proposed estimators are more efficient than some existing estimators. Data were simulated for study variable y and auxiliary variable x using R software for the analysis to support the claim. The result shows that MSE of the proposed estimators, y ̅_(pd,RSS)^* is smaller than the MSE of the existing estimators y ̅_pd^*,y ̅_Rd^*, y ̅_(R,RSS)^*,y ̅_(RSS,MM1)^* and y ̅_(RSS,MM2)^* and y ̅_(RSS,MM3)^* at ρ = −0.1,−0.2,0.1,0.2, hence, the proposed estimator performed better than the existing estimators. While the MSE of the proposed estimator yy ̅_(pd,RSS)^* is greater than the MSE of the existing estimators y ̅_pd^* and y ̅_Rd^* at ρ = -0.3 and 0.3. However, the proposed estimator y ̅_(pd,RSS)^* does not perform better than the estimators, y ̅_pd^*,and y ̅_Rd^* at ρ = -0.3 and 0.3. It was concluded that the proposed estimator was more efficient than a class of regression estimators and four existing ratio-type estimators based on RSS.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69336636","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}
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