Pub Date : 2018-03-29DOI: 10.6092/ISSN.1973-2201/6956
S. Zinodiny, Sadegh Rezaei, S. Nadarajah
The problem of estimating the mean matrix of a matrix-variate normal distribution with a covariance matrix is considered under two loss functions. We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function and hence show that the maximum likelihood estimator is inadmissible. We find a general class of minimax estimators. Also we give a class of estimators that improve on the maximum likelihood estimator under the second loss function and hence show that the maximum likelihood estimator is inadmissible.
{"title":"Minimax Estimation of the Mean Matrix of the Matrix Variate Normal Distribution under the Divergence Loss Function","authors":"S. Zinodiny, Sadegh Rezaei, S. Nadarajah","doi":"10.6092/ISSN.1973-2201/6956","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6956","url":null,"abstract":"The problem of estimating the mean matrix of a matrix-variate normal distribution with a covariance matrix is considered under two loss functions. We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function and hence show that the maximum likelihood estimator is inadmissible. We find a general class of minimax estimators. Also we give a class of estimators that improve on the maximum likelihood estimator under the second loss function and hence show that the maximum likelihood estimator is inadmissible.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43600872","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 : 2018-03-29DOI: 10.6092/ISSN.1973-2201/7241
Ayfer Ezgi Yilmaz
In square contingency tables, analysis of agreement between the row and column classifications is of interest. In such tables, the kappa-like statistics are used as a measure of reliability. In addition to the kappa coefficients, several authors discussed agreement in terms of log-linear models. Log-linear agreement models are suggested for use to summarize the degree of agreement between nominal variables. To analyze the agreement between ordinal categories, the association models with agreement parameter can be used. In the recent studies, researchers pay more attention to the assessment of agreement among more than two raters’ decisions, especially in areas of medical and behavioral sciences. This article focuses on the approaches to study of uniform and non-uniform association with inter-rater agreement for multi-raters with ordered categories. In this article, we proposed different modifications of association plus agreement models and illustrate use of the approaches over two numerical examples.
{"title":"Modeling Association plus Agreement among Multi-Raters for Ordered Categories","authors":"Ayfer Ezgi Yilmaz","doi":"10.6092/ISSN.1973-2201/7241","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7241","url":null,"abstract":"In square contingency tables, analysis of agreement between the row and column classifications is of interest. In such tables, the kappa-like statistics are used as a measure of reliability. In addition to the kappa coefficients, several authors discussed agreement in terms of log-linear models. Log-linear agreement models are suggested for use to summarize the degree of agreement between nominal variables. To analyze the agreement between ordinal categories, the association models with agreement parameter can be used. In the recent studies, researchers pay more attention to the assessment of agreement among more than two raters’ decisions, especially in areas of medical and behavioral sciences. This article focuses on the approaches to study of uniform and non-uniform association with inter-rater agreement for multi-raters with ordered categories. In this article, we proposed different modifications of association plus agreement models and illustrate use of the approaches over two numerical examples.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47844749","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 : 2018-03-29DOI: 10.6092/ISSN.1973-2201/7202
S. Nadarajah, E. Afuecheta, S. Chan
Copulas are used to specify dependence between two or more random variables. The last few years have seen a surge of developments of parametric models for copulas. Here, we provide an up-to-date and a comprehensive review of known parametric copulas as well as applications and open problems. This review is believed to be the first of its kind.
{"title":"A Compendium of Copulas","authors":"S. Nadarajah, E. Afuecheta, S. Chan","doi":"10.6092/ISSN.1973-2201/7202","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7202","url":null,"abstract":"Copulas are used to specify dependence between two or more random variables. The last few years have seen a surge of developments of parametric models for copulas. Here, we provide an up-to-date and a comprehensive review of known parametric copulas as well as applications and open problems. This review is believed to be the first of its kind.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48114548","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 : 2018-03-29DOI: 10.6092/ISSN.1973-2201/6779
V. Sharma
In this paper, we proposed Bayes estimators for estimating the parameters, reliability, hazard rate, mean time to failure from flexible Weibull distribution using Type-II hybrid censored sample. Bayes estimators have been obtained under squared error loss function assuming independent gamma prior distributions for the parameters. The maximum likelihood estimators along with asymptotic distributions have also been discussed. The performances of the estimators have been compared with respect to the various Type-II hybrid censoring schemes. For approximating the posteriors, we proposed the use of Markov chain Monte Carlo techniques such as Gibbs sampler and Metropolis-Hastings algorithm. Further, Bayesian One- andTwo-sample prediction problems have also been considered. A real data set has been analysed for illustration purposes.
{"title":"Estimation and Prediction for Type-II Hybrid Censored Data Follow Flexible Weibull Distribution","authors":"V. Sharma","doi":"10.6092/ISSN.1973-2201/6779","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6779","url":null,"abstract":"In this paper, we proposed Bayes estimators for estimating the parameters, reliability, hazard rate, mean time to failure from flexible Weibull distribution using Type-II hybrid censored sample. Bayes estimators have been obtained under squared error loss function assuming independent gamma prior distributions for the parameters. The maximum likelihood estimators along with asymptotic distributions have also been discussed. The performances of the estimators have been compared with respect to the various Type-II hybrid censoring schemes. For approximating the posteriors, we proposed the use of Markov chain Monte Carlo techniques such as Gibbs sampler and Metropolis-Hastings algorithm. Further, Bayesian One- andTwo-sample prediction problems have also been considered. A real data set has been analysed for illustration purposes.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48383225","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 : 2018-01-11DOI: 10.6092/ISSN.1973-2201/6856
Unnikrishnan N. Nair, S. Paduthol, Nidhi P. Ramesh
Among various characteristics of residual life, the concept of variance residual life in the univariate case has been extensively discussed in reliability literature. In the present work we extend this notion to the discrete multivariate case and study its properties. Different versions of classes of multivariate distributions based on the monotonicity of variance residual life are also presented along with some characterizations.
{"title":"Multivariate Variance Residual Life in Discrete Time","authors":"Unnikrishnan N. Nair, S. Paduthol, Nidhi P. Ramesh","doi":"10.6092/ISSN.1973-2201/6856","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6856","url":null,"abstract":"Among various characteristics of residual life, the concept of variance residual life in the univariate case has been extensively discussed in reliability literature. In the present work we extend this notion to the discrete multivariate case and study its properties. Different versions of classes of multivariate distributions based on the monotonicity of variance residual life are also presented along with some characterizations.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43691576","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 : 2018-01-11DOI: 10.6092/ISSN.1973-2201/6742
M. Samuh
In this paper, ranked set two-sample permutation test of comparing two-independent groups in terms of some measure of location is presented. Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the usual two-sample permutation test under simple random sampling and with the classical independent two-sample t -test.
{"title":"Ranked Set Two-Sample Permutation Test","authors":"M. Samuh","doi":"10.6092/ISSN.1973-2201/6742","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6742","url":null,"abstract":"In this paper, ranked set two-sample permutation test of comparing two-independent groups in terms of some measure of location is presented. Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the usual two-sample permutation test under simple random sampling and with the classical independent two-sample t -test.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45858424","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 : 2018-01-11DOI: 10.6092/ISSN.1973-2201/7134
C. Kumar, G. V. Anila
The normal and skew normal distributions are not adequate enough for modeling plurimodal data situations. In order to overcome this drawback of normal and skew normal distribution, Kumar and Anusree (2011) proposed a new class of distribution namely "the generalized mixture of standard normal and skew normal distributions (GMNSND)". In this paper we consider an extended version of the GMNSND as a wide class of plurimodal asymmetric normal distribution and investigate some of its important distributional properties. Location-scale extension of the proposed model is also defined and discussed the estimation of its parameters by method of maximum likelihood. Further, four real life data sets are considered for illustrating the usefulness of this model.
{"title":"On Some Aspects of a Generalized Asymmetric Normal Distribution","authors":"C. Kumar, G. V. Anila","doi":"10.6092/ISSN.1973-2201/7134","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7134","url":null,"abstract":"The normal and skew normal distributions are not adequate enough for modeling plurimodal data situations. In order to overcome this drawback of normal and skew normal distribution, Kumar and Anusree (2011) proposed a new class of distribution namely \"the generalized mixture of standard normal and skew normal distributions (GMNSND)\". In this paper we consider an extended version of the GMNSND as a wide class of plurimodal asymmetric normal distribution and investigate some of its important distributional properties. Location-scale extension of the proposed model is also defined and discussed the estimation of its parameters by method of maximum likelihood. Further, four real life data sets are considered for illustrating the usefulness of this model.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42080915","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 : 2018-01-11DOI: 10.6092/ISSN.1973-2201/6800
Girish Babu Moolath, K. Jayakumar
Using the quadratic transmutation map (QRTM) approach of Shaw and Buckley (2007) and the T - X family method by Alzaatreh et al. (2013b), we have developed a new family of distributions called T -transmuted X family of distributions. Many of the existing family of distributions are sub models of this family. As a special case, exponential transmuted exponential (ETE) distribution is studied in detail. The application and flexibility of this new distribution is illustrated using two real data sets.
{"title":"T-Transmuted X Family of Distributions","authors":"Girish Babu Moolath, K. Jayakumar","doi":"10.6092/ISSN.1973-2201/6800","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6800","url":null,"abstract":"Using the quadratic transmutation map (QRTM) approach of Shaw and Buckley (2007) and the T - X family method by Alzaatreh et al. (2013b), we have developed a new family of distributions called T -transmuted X family of distributions. Many of the existing family of distributions are sub models of this family. As a special case, exponential transmuted exponential (ETE) distribution is studied in detail. The application and flexibility of this new distribution is illustrated using two real data sets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43552083","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 : 2018-01-11DOI: 10.6092/ISSN.1973-2201/6965
Ajit Chaturvedi, Shantanu Vyas
Athree parameter Burr distribution is considered. Two measures of reliability are discussed. Point and interval estimation procedures are developed for the parameters, and reliability functions under type II and type I censoring. Two types of point estimators namely- uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are derived. Asymptotic variance-covariance matrix and confidence intervals for MLE’s are obtained. Testing procedures are also developed for various hypotheses.
{"title":"Estimation and Testing Procedures for the Reliability Functions of Three Parameter Burr Distribution under Censorings","authors":"Ajit Chaturvedi, Shantanu Vyas","doi":"10.6092/ISSN.1973-2201/6965","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6965","url":null,"abstract":"Athree parameter Burr distribution is considered. Two measures of reliability are discussed. Point and interval estimation procedures are developed for the parameters, and reliability functions under type II and type I censoring. Two types of point estimators namely- uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are derived. Asymptotic variance-covariance matrix and confidence intervals for MLE’s are obtained. Testing procedures are also developed for various hypotheses.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43375821","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 : 2017-10-24DOI: 10.6092/ISSN.1973-2201/6919
Fabrizio Ronchi, L. Salmaso, M. D. Dominicis, J. Illert
The experimental strategy developed thanks to the DOE methodology enhance innovation capability in the field of thermoforming production processes for active packaging. It is composed of three phases: i) material characterization, ii) production in pilot line, and iii) performance of final product. It allows selection of material, and correlation between control factors in production and performances of final product. Use of optimal designs allows reduction of number of tests, and in the meantime a full exploration of factorial space
{"title":"Optimal Designs to Develop and Support an Experimental Strategy on Innovation of Thermoforming Production Process","authors":"Fabrizio Ronchi, L. Salmaso, M. D. Dominicis, J. Illert","doi":"10.6092/ISSN.1973-2201/6919","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6919","url":null,"abstract":"The experimental strategy developed thanks to the DOE methodology enhance innovation capability in the field of thermoforming production processes for active packaging. It is composed of three phases: i) material characterization, ii) production in pilot line, and iii) performance of final product. It allows selection of material, and correlation between control factors in production and performances of final product. Use of optimal designs allows reduction of number of tests, and in the meantime a full exploration of factorial space","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2017-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42368492","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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