. In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R , and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior of the proposed approach in the wide range of simulation studies and in a case study of autistic and healthy individuals.
{"title":"Random Projection-Based Anderson-Darling Test for Random Fields","authors":"Yasser Al Zaim, Mohammad Reza Faridrohani","doi":"10.52547/jirss.20.2.1","DOIUrl":"https://doi.org/10.52547/jirss.20.2.1","url":null,"abstract":". In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R , and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior of the proposed approach in the wide range of simulation studies and in a case study of autistic and healthy individuals.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41338399","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}
. Sometimes in order to estimate population parameters such as mean and total values, we extract a random sample by cluster sampling method, and after completing sampling, we are interested in using the same sample to estimate the desired parameters in a subset of the population, which is said subpopulation. In this paper, we try to estimate subpopulation parameters in di ff erent cases when one-stage cluster sampling design is used.
{"title":"Estimation of Subpopulation Parameters in One-stage Cluster Sampling Design","authors":"Mostafa Hossaini, A. Rezaei Roknabadi","doi":"10.52547/jirss.20.2.65","DOIUrl":"https://doi.org/10.52547/jirss.20.2.65","url":null,"abstract":". Sometimes in order to estimate population parameters such as mean and total values, we extract a random sample by cluster sampling method, and after completing sampling, we are interested in using the same sample to estimate the desired parameters in a subset of the population, which is said subpopulation. In this paper, we try to estimate subpopulation parameters in di ff erent cases when one-stage cluster sampling design is used.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48800838","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}
. This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the parallel systems the reversed hazard, usual, convex transform, star, superadditive and dispersive orderings are studied. Also, we present a necessary and su ffi cient condition for being finiteness of the moments of the switched series and switched parallel systems.
{"title":"Preservation of Stochastic Orderings of Interdependent Series and Parallel Systems by Componentwise Switching to Exponentiated Models","authors":"H. Nadeb, H. Torabi","doi":"10.52547/jirss.20.2.117","DOIUrl":"https://doi.org/10.52547/jirss.20.2.117","url":null,"abstract":". This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the parallel systems the reversed hazard, usual, convex transform, star, superadditive and dispersive orderings are studied. Also, we present a necessary and su ffi cient condition for being finiteness of the moments of the switched series and switched parallel systems.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45947932","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}
Sahar Asili, A. Mohammadpour, O. Naghshineh Arjmand, M. Golalizazdedh
. Recently, some statistical studies have been done using the shape data. One of these studies is clustering shape data, which is the main topic of this paper. We are going to study some clustering algorithms on shape data and then introduce the best algorithm based on accuracy, speed, and scalability criteria. In addition, we propose a method for representing the shape data that facilitates and speeds up the shape clustering algorithms. Although the mentioned method is not very accurate, it is fast; therefore, it is useful for datasets with a high number of landmarks or observations, which take a long time to be clustered by means of other algorithms. It should be noted that this method is not new, but in this article we apply it in shape data analysis. clustering algorithms on five shape datasets.
{"title":"A Comparative Study of Some Clustering Algorithms on Shape Data","authors":"Sahar Asili, A. Mohammadpour, O. Naghshineh Arjmand, M. Golalizazdedh","doi":"10.52547/jirss.20.2.29","DOIUrl":"https://doi.org/10.52547/jirss.20.2.29","url":null,"abstract":". Recently, some statistical studies have been done using the shape data. One of these studies is clustering shape data, which is the main topic of this paper. We are going to study some clustering algorithms on shape data and then introduce the best algorithm based on accuracy, speed, and scalability criteria. In addition, we propose a method for representing the shape data that facilitates and speeds up the shape clustering algorithms. Although the mentioned method is not very accurate, it is fast; therefore, it is useful for datasets with a high number of landmarks or observations, which take a long time to be clustered by means of other algorithms. It should be noted that this method is not new, but in this article we apply it in shape data analysis. clustering algorithms on five shape datasets.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43886633","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}
. The two main goals in model selection are firstly introducing an approach to test homogeneity of several rival models and secondly selecting a set of reasonable models or estimating the best rival model to the true one. In this paper we extend Vuong’s method for several models to cluster them. Based on the working paper of Katayama (2008), we propose an approach to test whether rival models have expected relations. The multivariate extension of Vuong’s test gives the opportunity to examine some hypotheses about the rival models and their relations with respect to the unknown true model. On the other hand, the standard method of model selection provides an implementation of Occam’s razor, in which parsimony or simplicity is balanced against goodness of fit. Therefore, we are interested in clustering the rival models based on their divergence from the true model to select a suitable set of rival models. In this paper we have introduced two approaches to select suitable sets of rival models based on the multivariate extension of Vuong’s test and quasi clustering approach. MSC: 62F03, 62H30.
{"title":"Testing Several Rival Models Using the Extension of Vuong's Test and Quasi Clustering","authors":"A. Sayyareh","doi":"10.52547/jirss.20.2.43","DOIUrl":"https://doi.org/10.52547/jirss.20.2.43","url":null,"abstract":". The two main goals in model selection are firstly introducing an approach to test homogeneity of several rival models and secondly selecting a set of reasonable models or estimating the best rival model to the true one. In this paper we extend Vuong’s method for several models to cluster them. Based on the working paper of Katayama (2008), we propose an approach to test whether rival models have expected relations. The multivariate extension of Vuong’s test gives the opportunity to examine some hypotheses about the rival models and their relations with respect to the unknown true model. On the other hand, the standard method of model selection provides an implementation of Occam’s razor, in which parsimony or simplicity is balanced against goodness of fit. Therefore, we are interested in clustering the rival models based on their divergence from the true model to select a suitable set of rival models. In this paper we have introduced two approaches to select suitable sets of rival models based on the multivariate extension of Vuong’s test and quasi clustering approach. MSC: 62F03, 62H30.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49597587","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}
Nahid Ganjealivand, F. Ghapani, A. Zaherzadeh, F. Hormozinejad
. In this study, the stochastic restricted and unrestricted two-parameter estimators of fixed and random e ff ects are investigated in the linear mixed measurement error models. For this purpose, the asymptotic properties and then the comparisons under the criterion of mean squared error matrix ( MSEM ) are derived. Furthermore, the proposed methods are used for estimating the biasing parameters. Finally, a real data analysis and a simulation study are provided to evaluate the performance of the proposed estimators
{"title":"Stochastic Restricted Two-Parameter Estimator in Linear Mixed Measurement Error Models","authors":"Nahid Ganjealivand, F. Ghapani, A. Zaherzadeh, F. Hormozinejad","doi":"10.52547/jirss.20.2.79","DOIUrl":"https://doi.org/10.52547/jirss.20.2.79","url":null,"abstract":". In this study, the stochastic restricted and unrestricted two-parameter estimators of fixed and random e ff ects are investigated in the linear mixed measurement error models. For this purpose, the asymptotic properties and then the comparisons under the criterion of mean squared error matrix ( MSEM ) are derived. Furthermore, the proposed methods are used for estimating the biasing parameters. Finally, a real data analysis and a simulation study are provided to evaluate the performance of the proposed estimators","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48484873","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}
Jiju Gillariose, Lishamol Tomy, Farrukh Jamal, C. Chesneau
. Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some important distributions as special cases. Some properties of the new distribution are derived. The model parameters are estimated by the maximum likelihood method, with validation through a complete simulation study. The usefulness of the new model is illustrated via count-type real data sets. MSC:
{"title":"A Discrete Kumaraswamy Marshall-Olkin Exponential Distribution","authors":"Jiju Gillariose, Lishamol Tomy, Farrukh Jamal, C. Chesneau","doi":"10.52547/jirss.20.2.129","DOIUrl":"https://doi.org/10.52547/jirss.20.2.129","url":null,"abstract":". Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some important distributions as special cases. Some properties of the new distribution are derived. The model parameters are estimated by the maximum likelihood method, with validation through a complete simulation study. The usefulness of the new model is illustrated via count-type real data sets. MSC:","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43919022","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}
We study the blocks of interpoint distances, their distributions, correlations, independence and the homogeneity of their total variances. We discuss the exact and asymptotic distribution of the interpoint distances and their average under three models and provide connections between the correlation of interpoint distances with their vector correlation and test of sphericity. We discuss testing independence of the blocks based on the correlation of block interpoint distances. A homogeneity test of the total variances in each block and a simultaneous plot to visualize their relative ordering are presented.
{"title":"On the Blocks of Interpoint Distances","authors":"R. Modarres","doi":"10.52547/jirss.20.1.197","DOIUrl":"https://doi.org/10.52547/jirss.20.1.197","url":null,"abstract":"We study the blocks of interpoint distances, their distributions, correlations, independence and the homogeneity of their total variances. We discuss the exact and asymptotic distribution of the interpoint distances and their average under three models and provide connections between the correlation of interpoint distances with their vector correlation and test of sphericity. We discuss testing independence of the blocks based on the correlation of block interpoint distances. A homogeneity test of the total variances in each block and a simultaneous plot to visualize their relative ordering are presented.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43779937","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 recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in di ff erent fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function. MSC: 62B10, 62C05, 60E05, 60E15, 62N05, 94A15, 94A17. (CDF, PDF, SF, HR, MR, OR). The study of information properties of various types of mixtures involves assortments of information and divergence measures: Shannon entropy, KL, JS, Je ff reys, Chi-square, Rényi, Tsallis, and Je ff reys type symmetrized Tsallis divergences, Fisher information measure and Fisher information distance, KL type divergence between SFs, and expected L 1 -norm between cumulative hazards. Areas of applications covered include reliability (comparison of systems), econometrics (uncertainty and disagreements of forecasters), statistics (kernel estimation, exponential family, comparison of two normal means), and nonextensive statistical mechanics (escort distributions).
{"title":"Variants of Mixtures: Information Properties and Applications","authors":"Omid M. Ardakani, M. Asadi, N. Ebrahimi, E. Soofi","doi":"10.52547/jirss.20.1.27","DOIUrl":"https://doi.org/10.52547/jirss.20.1.27","url":null,"abstract":"In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in di ff erent fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function. MSC: 62B10, 62C05, 60E05, 60E15, 62N05, 94A15, 94A17. (CDF, PDF, SF, HR, MR, OR). The study of information properties of various types of mixtures involves assortments of information and divergence measures: Shannon entropy, KL, JS, Je ff reys, Chi-square, Rényi, Tsallis, and Je ff reys type symmetrized Tsallis divergences, Fisher information measure and Fisher information distance, KL type divergence between SFs, and expected L 1 -norm between cumulative hazards. Areas of applications covered include reliability (comparison of systems), econometrics (uncertainty and disagreements of forecasters), statistics (kernel estimation, exponential family, comparison of two normal means), and nonextensive statistical mechanics (escort distributions).","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46729957","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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