Pub Date : 2019-01-01DOI: 10.3844/jmssp.2019.259.272
V. Barbu, A. Karagrigoriou, A. Makrides
This work deals with multi-state systems modelled by means of semi-Markov processes. The sojourn times are seen to be independent not identically distributed random variables and assumed to belong to one of two different general classes of distributions so that the first class is closed under maxima and the second one is closed under minima. We obtain maximum likelihood estimators of the parameters of interest under several estimation schemes and investigate their asymptotic properties. Plug-in type estimators are furnished for various quantities related to the system under study.
{"title":"Estimation and Reliability for a Special Type of Semi-Markov Process","authors":"V. Barbu, A. Karagrigoriou, A. Makrides","doi":"10.3844/jmssp.2019.259.272","DOIUrl":"https://doi.org/10.3844/jmssp.2019.259.272","url":null,"abstract":"This work deals with multi-state systems modelled by means of semi-Markov processes. The sojourn times are seen to be independent not identically distributed random variables and assumed to belong to one of two different general classes of distributions so that the first class is closed under maxima and the second one is closed under minima. We obtain maximum likelihood estimators of the parameters of interest under several estimation schemes and investigate their asymptotic properties. Plug-in type estimators are furnished for various quantities related to the system under study.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"42 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87407585","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.2019.201.207
Afework Solomon
In his paper with the title, “The Homotopy Category is a Homotopy Category”, Arne Strom shows that the category Top of topo- logical spaces satisfies the axioms of an abstract homotopy category in the sense of Quillen. In this study, we show by examples that Quillen’s model structure on Top fails to capture some of the subtleties of classical homotopy theory and also, we show that the whole of classical homo-topy theory cannot be retrieved from the axiomatic approach of Quillen. Thus, we show that model category is an incomplete model of classical homotopy theory.
Arne Strom在其题为“同伦范畴是一个同伦范畴”的论文中，证明了拓扑空间的范畴顶满足Quillen意义上的抽象同伦范畴公理。在本研究中，我们通过实例表明，Quillen在Top上的模型结构未能捕捉到经典同伦理论的一些微妙之处，并且我们也表明，不能从Quillen的公理化方法中检索到整个经典同伦理论。因此，我们证明了模型范畴是经典同伦理论的不完全模型。
{"title":"A Note on “The Homotopy Category is a Homotopy Category”","authors":"Afework Solomon","doi":"10.3844/JMSSP.2019.201.207","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.201.207","url":null,"abstract":"In his paper with the title, “The Homotopy Category is a Homotopy Category”, Arne Strom shows that the category Top of topo- logical spaces satisfies the axioms of an abstract homotopy category in the sense of Quillen. In this study, we show by examples that Quillen’s model structure on Top fails to capture some of the subtleties of classical homotopy theory and also, we show that the whole of classical homo-topy theory cannot be retrieved from the axiomatic approach of Quillen. Thus, we show that model category is an incomplete model of classical homotopy theory.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"11 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82090459","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.2019.122.135
Mona Mustafa Elbiely
A new lifetime model with various shapes of the hazard rate function for modeling uni-modal and bimodal data sets is introduced and studied along with its statistical properties. Before using the maximum likelihood method for estimating the unknown model parameters, we assessed its performance via a simulation study. The flexibility of the new model is illustrated via plots of the probability and hazard rate functions for three real data applications.
{"title":"The Dual Exponentiated Weibull Model","authors":"Mona Mustafa Elbiely","doi":"10.3844/JMSSP.2019.122.135","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.122.135","url":null,"abstract":"A new lifetime model with various shapes of the hazard rate function for modeling uni-modal and bimodal data sets is introduced and studied along with its statistical properties. Before using the maximum likelihood method for estimating the unknown model parameters, we assessed its performance via a simulation study. The flexibility of the new model is illustrated via plots of the probability and hazard rate functions for three real data applications.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"17 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83006396","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.2019.44.54
Paranut Sukcharoen, S. Chongcharoen
In this paper, we proposed a new testing statistic for testing the equality of mean vectors from two multivariate normal populations when the covariance matrices are unknown and unequal in high–dimensional data. A new test is proposed based on the idea of keeping more information from the sample covariance matrices as much as possible. A proposed test is invariant under scalar transformations and location shifts. We showed that the asymptotic distribution of proposed statistic is standard normal distribution when number of random variables approach infinity. We also compared the performance of the proposed test with other three existing tests by the simulation study. The simulation results showed that the attained significance level of proposed test close to setting nominal significance level satisfactorily. The attained power of proposed test outperforms as the other comparative tests under form of covariance matrices considered which can be arranged to block diagonal matrix structure. The attained power becomes more powerful when the dimension increases for a given sample size or vice versa, or relationship level between random variables in each sample increases. Finally, the proposed test is also illustrated with an analysis of DNA microarray data.
{"title":"A Test on the Multivariate Behrens–Fisher Problem in High–Dimensional Data by Block Covariance Estimation","authors":"Paranut Sukcharoen, S. Chongcharoen","doi":"10.3844/JMSSP.2019.44.54","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.44.54","url":null,"abstract":"In this paper, we proposed a new testing statistic for testing the equality of mean vectors from two multivariate normal populations when the covariance matrices are unknown and unequal in high–dimensional data. A new test is proposed based on the idea of keeping more information from the sample covariance matrices as much as possible. A proposed test is invariant under scalar transformations and location shifts. We showed that the asymptotic distribution of proposed statistic is standard normal distribution when number of random variables approach infinity. We also compared the performance of the proposed test with other three existing tests by the simulation study. The simulation results showed that the attained significance level of proposed test close to setting nominal significance level satisfactorily. The attained power of proposed test outperforms as the other comparative tests under form of covariance matrices considered which can be arranged to block diagonal matrix structure. The attained power becomes more powerful when the dimension increases for a given sample size or vice versa, or relationship level between random variables in each sample increases. Finally, the proposed test is also illustrated with an analysis of DNA microarray data.","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":"83608798","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.2019.30.43
Mona Mustafa Elbiely, H. Yousof
In this work, we introduce a new flexible extension of the Inverse Weibull distribution. Some important mathematical properties of the proposed model are derived along with a numerical analysis of mean, variance, skewness and kurtosis measures of the proposed model. The performance of the maximum likelihood method is assesses via a comprehensive simulation studies in terms of mean squared errors. The new model is better than some other important competitive extensions of the Inverse Weibull in modeling the breaking stress data, the glass fibers data and the relief time data. Some plots are given to illustrate the suitability of the new model to fit the used data sets.
{"title":"A New Inverse Weibull Distribution: Properties and Applications","authors":"Mona Mustafa Elbiely, H. Yousof","doi":"10.3844/JMSSP.2019.30.43","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.30.43","url":null,"abstract":"In this work, we introduce a new flexible extension of the Inverse Weibull distribution. Some important mathematical properties of the proposed model are derived along with a numerical analysis of mean, variance, skewness and kurtosis measures of the proposed model. The performance of the maximum likelihood method is assesses via a comprehensive simulation studies in terms of mean squared errors. The new model is better than some other important competitive extensions of the Inverse Weibull in modeling the breaking stress data, the glass fibers data and the relief time data. Some plots are given to illustrate the suitability of the new model to fit the used data sets.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"14 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":"78400035","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.2019.86.98
T. Antczak, Najeeb Abdulaleem
n this study, the class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. For such (not necessarily) differentiable multicriteria optimization problems, two E-Lagrange functions and their E-saddle points are defined. Then the so-called E-saddle point criteria are established for such (not necessarily) differentiable multiobjective programming problems with E-differentiable E-convex functions.
{"title":"E-Saddle Point Criteria for E-differentiable Vector Optimization Problems with Inequality and Equality Constraints","authors":"T. Antczak, Najeeb Abdulaleem","doi":"10.3844/JMSSP.2019.86.98","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.86.98","url":null,"abstract":"n this study, the class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. For such (not necessarily) differentiable multicriteria optimization problems, two E-Lagrange functions and their E-saddle points are defined. Then the so-called E-saddle point criteria are established for such (not necessarily) differentiable multiobjective programming problems with E-differentiable E-convex functions.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"50 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76771194","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.2019.65.69
A. Alanzi, Naser A. Alodat, Ahmad Mohammad Qazza
In this paper we have developed an alternative estimator for the Probability Proportional to Size (PPS) with replacement sampling scheme when certain characteristics under study are positively correlated with the selection probability. An analogue to the well-known superpopulation model for finite population is also suggested, using which, we compare the proposed estimator with Hansen and Hurwitz estimator. Finally, an empirical investigation of the performance of the propose estimator has also been made.
{"title":"Modification on PPS Sample Scheme with Replacement","authors":"A. Alanzi, Naser A. Alodat, Ahmad Mohammad Qazza","doi":"10.3844/JMSSP.2019.65.69","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.65.69","url":null,"abstract":"In this paper we have developed an alternative estimator for the Probability Proportional to Size (PPS) with replacement sampling scheme when certain characteristics under study are positively correlated with the selection probability. An analogue to the well-known superpopulation model for finite population is also suggested, using which, we compare the proposed estimator with Hansen and Hurwitz estimator. Finally, an empirical investigation of the performance of the propose estimator has also been made.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"96 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74684295","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.2019.146.157
Hisham A. H. Elsayed, H. Yousof
In this study, new version from the Nadarajah Haghighi model is proposed. The introduced model has a failure rate function that may change in different directions. Statistical properties of the new density function are derived along with the analysis of variance, Skewness and Kurtosis. Parameter estimates are obtained by the method of maximum likelihood. Illustration of real data set was employed to measure flexibility of the new model. A simulation study was executed to test performance of the proposed version.
{"title":"The Burr X Nadarajah Haghighi Distribution: Statistical Properties and Application to the Exceedances of Flood Peaks Data","authors":"Hisham A. H. Elsayed, H. Yousof","doi":"10.3844/JMSSP.2019.146.157","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.146.157","url":null,"abstract":"In this study, new version from the Nadarajah Haghighi model is proposed. The introduced model has a failure rate function that may change in different directions. Statistical properties of the new density function are derived along with the analysis of variance, Skewness and Kurtosis. Parameter estimates are obtained by the method of maximum likelihood. Illustration of real data set was employed to measure flexibility of the new model. A simulation study was executed to test performance of the proposed version.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"63 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86827032","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.2019.136.145
J. V. Zyl, J. Tubbs
The objective of this paper is to consider an indirect comparison between treatments B and C when each have been compared directly to treatment A in separate studies. Problems of this type are common in Network Meta-Analysis (NMA). A commonly used method assumes that the underlying data, Y, are normally distributed and µ = E(Y) is the measure of clinical effectiveness. The normal assumption is often violated. In addition, the sample sizes are not necessarily large. These conditions challenge the concept that a single location parameter, such as, the mean or median should be used as the measure of clinical effectiveness in the analysis. In this paper, we present an alternative approach where the Area Under the ROC Curve (AUC) is used as the measure of clinical effectiveness. Since the normal distribution may be uncertain, we use a distribution-free Bayesian mixtures of Finite Polya Trees (MFPT) model with the AUC in order to make the indirect comparison.
{"title":"A Distribution-Free Bayesian Approach for Indirect Comparisons","authors":"J. V. Zyl, J. Tubbs","doi":"10.3844/jmssp.2019.136.145","DOIUrl":"https://doi.org/10.3844/jmssp.2019.136.145","url":null,"abstract":"The objective of this paper is to consider an indirect comparison between treatments B and C when each have been compared directly to treatment A in separate studies. Problems of this type are common in Network Meta-Analysis (NMA). A commonly used method assumes that the underlying data, Y, are normally distributed and µ = E(Y) is the measure of clinical effectiveness. The normal assumption is often violated. In addition, the sample sizes are not necessarily large. These conditions challenge the concept that a single location parameter, such as, the mean or median should be used as the measure of clinical effectiveness in the analysis. In this paper, we present an alternative approach where the Area Under the ROC Curve (AUC) is used as the measure of clinical effectiveness. Since the normal distribution may be uncertain, we use a distribution-free Bayesian mixtures of Finite Polya Trees (MFPT) model with the AUC in order to make the indirect comparison.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"24 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87219955","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.2019.273.279
E. Kalligeris, A. Karagrigoriou, Kostantinos Ladopoulos, C. Parpoula
n this paper we introduce adjusted transformation methods for off-line quality control. The proposed methods result in proper performance measures for the determination of the controllable factors that affect the mean and variability of the response variable of interest. The details of the proposed adjusted transformations are provided and compared with the well-known Box and Coxtransformation and the safeguard method of Logothetis. The performance abilities of the proposed methodology are demonstrated on quality control data, considering both a real dataset and a simulated one.
{"title":"Adjusted Transformation Methods for Reproduction Quality Control","authors":"E. Kalligeris, A. Karagrigoriou, Kostantinos Ladopoulos, C. Parpoula","doi":"10.3844/jmssp.2019.273.279","DOIUrl":"https://doi.org/10.3844/jmssp.2019.273.279","url":null,"abstract":"n this paper we introduce adjusted transformation methods for off-line quality control. The proposed methods result in proper performance measures for the determination of the controllable factors that affect the mean and variability of the response variable of interest. The details of the proposed adjusted transformations are provided and compared with the well-known Box and Coxtransformation and the safeguard method of Logothetis. The performance abilities of the proposed methodology are demonstrated on quality control data, considering both a real dataset and a simulated one.","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":"88971070","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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