Pub Date : 2019-01-01DOI: 10.3844/JMSSP.2019.218.224
A. Artemiou
In this work we try to address the imbalance of the number of points which naturally occurs when slicing the response in Sufficient Dimension Reduction methods (SDR). Specifically, some recently proposed support vector machine based (SVM-based) methodology suffers a lot more due to the properties of the SVM algorithm. We target a recently proposed algorithm called Principal LqSVM and we propose the reweighting based on a different cost. We demonstrate that our reweighted proposal works better than the original algorithm in simulated and real data.
{"title":"Cost-based Reweighting for Principal Lq Support Vector Machines for Sufficient Dimension Reduction","authors":"A. Artemiou","doi":"10.3844/JMSSP.2019.218.224","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.218.224","url":null,"abstract":"In this work we try to address the imbalance of the number of points which naturally occurs when slicing the response in Sufficient Dimension Reduction methods (SDR). Specifically, some recently proposed support vector machine based (SVM-based) methodology suffers a lot more due to the properties of the SVM algorithm. We target a recently proposed algorithm called Principal LqSVM and we propose the reweighting based on a different cost. We demonstrate that our reweighted proposal works better than the original algorithm in simulated and real data.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"36 12 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76549288","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 : 2019-01-01DOI: 10.3844/JMSSP.2019.12.21
Julio César Alonso, Daniela Estrada
In this work, we assess the power and size of eight normality tests underthe assumption that errors follow a GARCH (1, 1) process by using MonteCarlo simulations. Four results stand out. First, the presence of a GARCH(1, 1) process increases the probability of making type I error. Second, Pearsonnormality test is recommended if it is assumed that errors follow a GARCH(1, 1) process. Third, statistical power varies depending on the type of heteroscedasticity and distribution considered. Fourth, normality tests have lowstatistical power and size (less than or equal to the nominal level) for smalland homoscedastic samples.
{"title":"Statistical Size and Power of Eight Normality Tests in Presence of GARCH (1 1) Errors","authors":"Julio César Alonso, Daniela Estrada","doi":"10.3844/JMSSP.2019.12.21","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.12.21","url":null,"abstract":"In this work, we assess the power and size of eight normality tests underthe assumption that errors follow a GARCH (1, 1) process by using MonteCarlo simulations. Four results stand out. First, the presence of a GARCH(1, 1) process increases the probability of making type I error. Second, Pearsonnormality test is recommended if it is assumed that errors follow a GARCH(1, 1) process. Third, statistical power varies depending on the type of heteroscedasticity and distribution considered. Fourth, normality tests have lowstatistical power and size (less than or equal to the nominal level) for smalland homoscedastic samples.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89857420","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 : 2019-01-01DOI: 10.3844/JMSSP.2019.196.200
J. Césars, S. P. Nuiro, J. Vaillant
We consider a Stochastic Differential Equation (SDE) driven by a Wiener process and a Poisson measure. This latter measure is associated with a sequence of identically distributed jump amplitudes. Properties of the SDE solution are presented with respect to the associated Wiener and Poisson processes. An algorithm is provided allowing exact numerical simulations of such SDE and implementable within R environment. Statistical inference tools are presented and applied to hydrology data.
{"title":"Statistical Inference on a Black-Scholes Model with Jumps. Application in Hydrology","authors":"J. Césars, S. P. Nuiro, J. Vaillant","doi":"10.3844/JMSSP.2019.196.200","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.196.200","url":null,"abstract":"We consider a Stochastic Differential Equation (SDE) driven by a Wiener process and a Poisson measure. This latter measure is associated with a sequence of identically distributed jump amplitudes. Properties of the SDE solution are presented with respect to the associated Wiener and Poisson processes. An algorithm is provided allowing exact numerical simulations of such SDE and implementable within R environment. Statistical inference tools are presented and applied to hydrology data.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"7 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73879717","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}
In this work, we introduce and study a new alternative Lomax model. The maximum likelihood method is used to estimate the unknown model parameters. We show empirically the importance and wide flexibility of the new model in modeling two types of failure times data sets. The new model is much better than the gamma Lomax, exponentiated Lomax, beta Lomax and Lomax models so the new model is a good alternative to these models.
{"title":"A New Extension of the Lomax Distribution with Statistical Properties and Applications to Failure and Service Times Data Sets","authors":"Mohamed K. A. Refaie","doi":"10.3844/JMSSP.2019.1.11","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.1.11","url":null,"abstract":"In this work, we introduce and study a new alternative Lomax model. The maximum likelihood method is used to estimate the unknown model parameters. We show empirically the importance and wide flexibility of the new model in modeling two types of failure times data sets. The new model is much better than the gamma Lomax, exponentiated Lomax, beta Lomax and Lomax models so the new model is a good alternative to these models.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"16 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84102545","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 : 2018-12-21DOI: 10.3844/JMSSP.2018.253.260
Miss Lei Wang
In this study, the focus is to collect and summarize various advanced forecasting models for multivariate time series dataset. We have discussed about the inherent forecasting strengths and weaknesses related to these time series modelings. Also, the main section deal with the experience of using such data in econometric analysis. Besides, the implementation of SAS and R softwares improve the parameter estimation and forecasting accuracy. Eventually, we evaluated these forecasting models by different criterions and select the best one for the future tendency of land market value.
{"title":"Advanced Multivariate Time Series Forecasting Models","authors":"Miss Lei Wang","doi":"10.3844/JMSSP.2018.253.260","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.253.260","url":null,"abstract":"In this study, the focus is to collect and summarize various advanced forecasting models for multivariate time series dataset. We have discussed about the inherent forecasting strengths and weaknesses related to these time series modelings. Also, the main section deal with the experience of using such data in econometric analysis. Besides, the implementation of SAS and R softwares improve the parameter estimation and forecasting accuracy. Eventually, we evaluated these forecasting models by different criterions and select the best one for the future tendency of land market value.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"50 1","pages":"253-260"},"PeriodicalIF":0.3,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77823031","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 : 2018-11-12DOI: 10.3844/JMSSP.2018.219.231
P. Williamson
Bayesian Credible Intervals are proposed for a Poisson mean. These intervals are compared to five classical confidence intervals found in the literature. A simulation study is performed to compare the procedures using two different criteria and it is attempted to determine which of the procedures performs best for various values of the parameter and sample size. Estimation of the number of three-point shot attempts and three-point shot makes by the San Antonio Spurs is given as an example.
{"title":"Bayesian Approach to the Estimation of a Poisson Mean with Application to NBA Three Point Attempts","authors":"P. Williamson","doi":"10.3844/JMSSP.2018.219.231","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.219.231","url":null,"abstract":"Bayesian Credible Intervals are proposed for a Poisson mean. These intervals are compared to five classical confidence intervals found in the literature. A simulation study is performed to compare the procedures using two different criteria and it is attempted to determine which of the procedures performs best for various values of the parameter and sample size. Estimation of the number of three-point shot attempts and three-point shot makes by the San Antonio Spurs is given as an example.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"14 1","pages":"219-231"},"PeriodicalIF":0.3,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81681039","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}
In this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which is a variant of type theory and the foundation for the proof assistant COQ. In a type theory every term and proposition should have a type, so in our formalizations we assign an appropriate type to each object in order to create a framework where further development of formalized probability theory will be possible. Our formalizations are based on mathematical results developed in the COQ standard library; we use mainly the parts with logic and formalized real analysis. In the future we aim to create COQ coding for our formalizations of probability concepts and theorems. In this paper the definitions and some proofs are presented as flag-style derivations while other proofs are more informal.
{"title":"Formalizing Probability Concepts in a Type Theory","authors":"F. Kachapova","doi":"10.3844/OFSP.12176","DOIUrl":"https://doi.org/10.3844/OFSP.12176","url":null,"abstract":"In this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which is a variant of type theory and the foundation for the proof assistant COQ. In a type theory every term and proposition should have a type, so in our formalizations we assign an appropriate type to each object in order to create a framework where further development of formalized probability theory will be possible. Our formalizations are based on mathematical results developed in the COQ standard library; we use mainly the parts with logic and formalized real analysis. In the future we aim to create COQ coding for our formalizations of probability concepts and theorems. In this paper the definitions and some proofs are presented as flag-style derivations while other proofs are more informal.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"8 1","pages":"209-218"},"PeriodicalIF":0.3,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84452445","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 : 2018-06-27DOI: 10.3844/JMSSP.2018.175.182
Haridas kumar Das, Nasim Reza
This paper is based on the analytic and computational solution procedures of Grobner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving a system of polynomial equations (linear and nonlinear) with a finite number of solutions extending the idea of Grobner basis. Finally we explore the idea of Grobner basis for coloring the vertices of a given graph. We illustrate the stated results through a number of examples. Moreover, as for auxilary and making comparison with the analytic results, we use Mathematica 9.0.1 to develop some computer algebra.
{"title":"On Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph Coloring","authors":"Haridas kumar Das, Nasim Reza","doi":"10.3844/JMSSP.2018.175.182","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.175.182","url":null,"abstract":"This paper is based on the analytic and computational solution procedures of Grobner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving a system of polynomial equations (linear and nonlinear) with a finite number of solutions extending the idea of Grobner basis. Finally we explore the idea of Grobner basis for coloring the vertices of a given graph. We illustrate the stated results through a number of examples. Moreover, as for auxilary and making comparison with the analytic results, we use Mathematica 9.0.1 to develop some computer algebra.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"92 1","pages":"175-182"},"PeriodicalIF":0.3,"publicationDate":"2018-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83752330","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 : 2018-06-12DOI: 10.3844/JMSSP.2018.167.174
S. Assar
A new distribution, called odds generalized exponential-power Lomax distribution is suggested for modeling lifetime data. Some structural properties of the new distribution including; quantiles, Renyi entropy, moments and distribution of order statistics are provided. The model parameters of the new distribution are estimated by the maximum likelihood method. Finally, applications to two real data sets are analyzed to illustrate the importance of the new distribution compared with some known distributions.
{"title":"On Odds Generalized Exponential-Power Lomax Distribution","authors":"S. Assar","doi":"10.3844/JMSSP.2018.167.174","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.167.174","url":null,"abstract":"A new distribution, called odds generalized exponential-power Lomax distribution is suggested for modeling lifetime data. Some structural properties of the new distribution including; quantiles, Renyi entropy, moments and distribution of order statistics are provided. The model parameters of the new distribution are estimated by the maximum likelihood method. Finally, applications to two real data sets are analyzed to illustrate the importance of the new distribution compared with some known distributions.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"61 1","pages":"167-174"},"PeriodicalIF":0.3,"publicationDate":"2018-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85227199","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 : 2018-05-31DOI: 10.3844/JMSSP.2018.72.78
A. Esi, N. Subramanian, V. Khan
Corresponding Author: Ayhan Esi Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey Email: aesi23@hotmail.com Abstract: We introduced and studied the concept of I-convergence of triple sequences in metric spaces where I is an ideal. The concept of Iconvergence has a wide application in the field of number theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article, we introduce rough intuitionistic fuzzy Lacunary ideal convergent of triple sequence spaces via zwier operators. We discuss general topological properties.
{"title":"The Rough Intuitionistic Fuzzy Zweier Lacunary Ideal Convergence of Triple Sequence Spaces","authors":"A. Esi, N. Subramanian, V. Khan","doi":"10.3844/JMSSP.2018.72.78","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.72.78","url":null,"abstract":"Corresponding Author: Ayhan Esi Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey Email: aesi23@hotmail.com Abstract: We introduced and studied the concept of I-convergence of triple sequences in metric spaces where I is an ideal. The concept of Iconvergence has a wide application in the field of number theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article, we introduce rough intuitionistic fuzzy Lacunary ideal convergent of triple sequence spaces via zwier operators. We discuss general topological properties.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"6 1","pages":"72-78"},"PeriodicalIF":0.3,"publicationDate":"2018-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81367321","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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