In this paper a new method of introducing an additional parameter to a continuous distribution is proposed, which leads to a new class of distributions, called the weighted exponentiated family. A special sub-model is discussed. General expressions for some of the mathematical properties of this class such as the moments, quantile function, generating function and order statistics are derived; and certain characterizations are also discussed. To estimate the model parameters, the method of maximum likelihood is applied. A simulation study is carried out to assess the finite sample behavior of the maximum likelihood estimators. Finally, the usefulness of the proposed method via two applications to real data sets is illustrated.
{"title":"The Weighted Exponentiated Family of Distributions: Properties, Applications and Characterizations","authors":"Zubair Ahmad, G. Hamedani, M. Elgarhy","doi":"10.29252/jirss.19.1.209","DOIUrl":"https://doi.org/10.29252/jirss.19.1.209","url":null,"abstract":"In this paper a new method of introducing an additional parameter to a continuous distribution is proposed, which leads to a new class of distributions, called the weighted exponentiated family. A special sub-model is discussed. General expressions for some of the mathematical properties of this class such as the moments, quantile function, generating function and order statistics are derived; and certain characterizations are also discussed. To estimate the model parameters, the method of maximum likelihood is applied. A simulation study is carried out to assess the finite sample behavior of the maximum likelihood estimators. Finally, the usefulness of the proposed method via two applications to real data sets is illustrated.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"19 1","pages":"209-228"},"PeriodicalIF":0.4,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41861014","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 propose a copula-based index to detect the reflection asymmetry in trivariate distributions. The proposed index is based on the definition of directional reflection asymmetry over the set of directions. We derive the asymptotic distribution of the rank-based estimator of the proposed index. The value of the index and the direction in which the asymmetry occurs are easily computed, and we illustrate it with a simulation study and a real data analysis.
{"title":"A Copula-based Index to Measure Directional Reflection Asymmetry for Trivariate Copulas","authors":"A. Dolati, Ahmad Alikhani-Vafa","doi":"10.29252/JIRSS.18.2.139","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.139","url":null,"abstract":"We propose a copula-based index to detect the reflection asymmetry in trivariate distributions. The proposed index is based on the definition of directional reflection asymmetry over the set of directions. We derive the asymptotic distribution of the rank-based estimator of the proposed index. The value of the index and the direction in which the asymmetry occurs are easily computed, and we illustrate it with a simulation study and a real data analysis.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"139-153"},"PeriodicalIF":0.4,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44224210","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}
{"title":"برآوردگرهای انقباضی تابع چگالی احتمال تحت وابستگی","authors":"مرضیه محمودی, محمد آرشی, احمد نزاکتی","doi":"10.29252/JIRSS.18.2.173","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.173","url":null,"abstract":"","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"173-197"},"PeriodicalIF":0.4,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69861444","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 introduces a functional mixed effect random model to model spatial data. In this model, the spatial locations form the index set, while the contributing effects to the response variable are set as a linear mixture of fixed and random effects. These fixed and random effects are linear combinations of L2 functions and random elements, respectively. However, the corresponding linear factors depend on the spatial location variable. Therefore, we develop estimation procedures to estimate the fixed and random coefficients, using spatial functional principal component analysis. Then, we perform prediction by adapting the functional universal kriging method to our model.
{"title":"On a Linear Functional Mixed Effect Model for Spatial Data","authors":"R. Nasirzadeh, Jeorge Mateu, A. Soltani","doi":"10.29252/JIRSS.18.2.115","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.115","url":null,"abstract":"This paper introduces a functional mixed effect random model to model spatial data. In this model, the spatial locations form the index set, while the contributing effects to the response variable are set as a linear mixture of fixed and random effects. These fixed and random effects are linear combinations of L2 functions and random elements, respectively. However, the corresponding linear factors depend on the spatial location variable. Therefore, we develop estimation procedures to estimate the fixed and random coefficients, using spatial functional principal component analysis. Then, we perform prediction by adapting the functional universal kriging method to our model.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"115-137"},"PeriodicalIF":0.4,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43804759","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 article, the tests on parallelism, equal intercept and sets of lines intersected at a fixed value for a set of r simple linear models or a set of r linearizable regression models are generalized to the multivariate case, r = 2, 3, . . . ,R. Likewise, the normality hypothesis is replaced assuming an elliptical matrix variate distribution, concluding that the tests obtained under normality are valid and are invariant under the whole family of elliptical matrix variate distributions. Finally, an application in an agricultural acarology context is provided.
{"title":"Tests about a Set of Multivariate Simple Linear Models","authors":"J. A. Díaz-García, O. Martínez-Jaime","doi":"10.29252/JIRSS.18.2.199","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.199","url":null,"abstract":"In this article, the tests on parallelism, equal intercept and sets of lines intersected at a fixed value for a set of r simple linear models or a set of r linearizable regression models are generalized to the multivariate case, r = 2, 3, . . . ,R. Likewise, the normality hypothesis is replaced assuming an elliptical matrix variate distribution, concluding that the tests obtained under normality are valid and are invariant under the whole family of elliptical matrix variate distributions. Finally, an application in an agricultural acarology context is provided.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"199-220"},"PeriodicalIF":0.4,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41736413","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}
اعظم خیری, محمد امینی, هادی جباری نوغابی, ابوالقاسم بزرگ نیا
In this paper, the kernel distribution function estimator for negative superadditive dependent (NSD) random variables is studied. The exponential inequalities and exponential rate for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth is determined using the mean squared error and is found to be the same as that in the independent identically distributed case. A simulation study to examine the behavior of the kernel and empirical estimators is given. Moreover, a real data set in hydrology is analyzed to demonstrate the structure of negative superadditive dependence, and as a result, the kernel distribution function estimator of the data is investigated.
{"title":"Convergence Rate for Estimator of Distribution Function under NSD Assumption with an Application","authors":"اعظم خیری, محمد امینی, هادی جباری نوغابی, ابوالقاسم بزرگ نیا","doi":"10.29252/JIRSS.18.2.21","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.21","url":null,"abstract":"In this paper, the kernel distribution function estimator for negative superadditive dependent (NSD) random variables is studied. The exponential inequalities and exponential rate for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth is determined using the mean squared error and is found to be the same as that in the independent identically distributed case. A simulation study to examine the behavior of the kernel and empirical estimators is given. Moreover, a real data set in hydrology is analyzed to demonstrate the structure of negative superadditive dependence, and as a result, the kernel distribution function estimator of the data is investigated.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"21-37"},"PeriodicalIF":0.4,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48606730","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}
M. Tamandi, Hossein Negarestani, A. Jamalizadeh, Mehdi Amiri
This paper presents a skew-normal mean-variance mixture based on BirnbaumSaunders (SNMVBS) distribution and discusses some of its key properties. The SNMVBS distribution can be thought as a flexible extension of the normal mean-variance mixture based on Birnbaum-Saunders (NMVBS) distribution as it possesses one additional shape parameter for providing more flexibility with skewness and kurtosis. Next, we develop a computationally feasible ECM algorithm for the maximum likelihood estimation of the model parameters. Asymptotic standard errors of the ML estimates are obtained through an approximation of the observed information matrix. Finally, the usefulness of the proposed model and its fitting method are illustrated through a Monte-Carlo simulation as well as three real-life datasets.
{"title":"Skew-normal Mean-variance Mixture of Birnbaum-Saunders Distribution","authors":"M. Tamandi, Hossein Negarestani, A. Jamalizadeh, Mehdi Amiri","doi":"10.29252/JIRSS.18.2.87","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.87","url":null,"abstract":"This paper presents a skew-normal mean-variance mixture based on BirnbaumSaunders (SNMVBS) distribution and discusses some of its key properties. The SNMVBS distribution can be thought as a flexible extension of the normal mean-variance mixture based on Birnbaum-Saunders (NMVBS) distribution as it possesses one additional shape parameter for providing more flexibility with skewness and kurtosis. Next, we develop a computationally feasible ECM algorithm for the maximum likelihood estimation of the model parameters. Asymptotic standard errors of the ML estimates are obtained through an approximation of the observed information matrix. Finally, the usefulness of the proposed model and its fitting method are illustrated through a Monte-Carlo simulation as well as three real-life datasets.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"87-113"},"PeriodicalIF":0.4,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44309154","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}
. Testing exponentiality has long been an interesting issue in statistical infer-ences. The present article is based on a modified measure of distance between two distributions. The proposed new measure is similar to the Kullback-Leibler divergence and it is related to the Lin-Wong divergence applied on the residual lifetime data. A modified measure is developed here which is a consistent test statistic for testing the hypothesis of exponentiality against some alternatives. First, we consider a method similar to Vasicek’s and Correa’s techniques of estimating the density function in order to construct statistic for LW divergence. Then the critical values of the test are computed, using a Monte-Carlo simulation method. Also, we find the di (cid:11) erences of exponential distribution detection power between the proposed test and other tests. It is shown that the proposed test performs better than other tests of exponentiality when the hazard rate is in the form of an increasing function. Finally, a case of application of the proposed test is shown through two illustrative examples. tic, Exponentiality Test, Goodness of Fit Testing, Kolmogorov-Smirnov Statistic, Kullback-Leibler Divergence, Lin-Wong Divergence, Residual Lifetime Data, Vasicek’s Technique, Zhang’s Statistics. MSC: 94A17; 62G10.
{"title":"Testing Exponentiality Based on the Lin Wong Divergence on the Residual Lifetime Data","authors":"M. Khalili, A. Habibirad, F. Yousefzadeh","doi":"10.29252/JIRSS.18.2.39","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.39","url":null,"abstract":". Testing exponentiality has long been an interesting issue in statistical infer-ences. The present article is based on a modified measure of distance between two distributions. The proposed new measure is similar to the Kullback-Leibler divergence and it is related to the Lin-Wong divergence applied on the residual lifetime data. A modified measure is developed here which is a consistent test statistic for testing the hypothesis of exponentiality against some alternatives. First, we consider a method similar to Vasicek’s and Correa’s techniques of estimating the density function in order to construct statistic for LW divergence. Then the critical values of the test are computed, using a Monte-Carlo simulation method. Also, we find the di (cid:11) erences of exponential distribution detection power between the proposed test and other tests. It is shown that the proposed test performs better than other tests of exponentiality when the hazard rate is in the form of an increasing function. Finally, a case of application of the proposed test is shown through two illustrative examples. tic, Exponentiality Test, Goodness of Fit Testing, Kolmogorov-Smirnov Statistic, Kullback-Leibler Divergence, Lin-Wong Divergence, Residual Lifetime Data, Vasicek’s Technique, Zhang’s Statistics. MSC: 94A17; 62G10.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42157345","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}
{"title":"Monte Carlo Comparison of Five Birnbaum-Saunders Distribution Goodness-of-fit Tests using Different Entropy Estimates","authors":"Saeed Darijani, Hojatollah Zakerzade, H. Torabi","doi":"10.29252/jirss.18.2.1","DOIUrl":"https://doi.org/10.29252/jirss.18.2.1","url":null,"abstract":"","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69861317","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 article addresses the problem of Bayesian shrinkage estimation for the Rayleigh scale parameter based on record values under the reflected gamma loss (RGL) function. A class of Bayesian shrinkage estimators using prior point information is constructed. The risk functions of the maximum likelihood estimator (MLE) and proposed Bayesian shrinkage estimator are derived under the RGL function. The performance of Bayesian shrinkage estimator is compared with the MLE numerically and graphically. One data set has been analyzed to illustrate the performance of the Bayesian shrinkage estimator.
{"title":"Performance of a Class of Bayes Shrinkage Estimators Based on Rayleigh Record Data under Reflected Gamma Loss Function","authors":"M. N. Qomi, S. Dey, Monir Fathollahi","doi":"10.29252/JIRSS.18.2.155","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.155","url":null,"abstract":"This article addresses the problem of Bayesian shrinkage estimation for the Rayleigh scale parameter based on record values under the reflected gamma loss (RGL) function. A class of Bayesian shrinkage estimators using prior point information is constructed. The risk functions of the maximum likelihood estimator (MLE) and proposed Bayesian shrinkage estimator are derived under the RGL function. The performance of Bayesian shrinkage estimator is compared with the MLE numerically and graphically. One data set has been analyzed to illustrate the performance of the Bayesian shrinkage estimator.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"18 1","pages":"155-172"},"PeriodicalIF":0.4,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46287084","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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