. This paper develops a new class of spatio-temporal process models that can simultaneously capture skewness and non-stationarity. The proposed approach which is based on using the closed skew-normal distribution in the low-rank representation of stochastic processes, has several favorable properties. In particular, it greatly reduces the dimension of the spatio-temporal latent variables and induces flexible correlation structures. Bayesian analysis of the model is implemented through a Gibbs MCMC algorithm which incorporates a version of the Kalman filtering algorithm. All fully conditional posterior distributions have closed forms which show another advanta-geous property of the proposed model. We demonstrate the e (cid:14) ciency of our model through an extensive simulation study and an application to a real data set comprised of precipitation measurements.
{"title":"A Skew-Gaussian Spatio-Temporal Process with Non-Stationary Correlation Structure","authors":"Zahra Barzegar, F. Rivaz, M. J. Khaledi","doi":"10.29252/JIRSS.18.2.63","DOIUrl":"https://doi.org/10.29252/JIRSS.18.2.63","url":null,"abstract":". This paper develops a new class of spatio-temporal process models that can simultaneously capture skewness and non-stationarity. The proposed approach which is based on using the closed skew-normal distribution in the low-rank representation of stochastic processes, has several favorable properties. In particular, it greatly reduces the dimension of the spatio-temporal latent variables and induces flexible correlation structures. Bayesian analysis of the model is implemented through a Gibbs MCMC algorithm which incorporates a version of the Kalman filtering algorithm. All fully conditional posterior distributions have closed forms which show another advanta-geous property of the proposed model. We demonstrate the e (cid:14) ciency of our model through an extensive simulation study and an application to a real data set comprised of precipitation measurements.","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":"69861462","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 is going to introduce a new method for ranked set sampling with multiple criteria. The method is based on a version of ranked set sampling, introduced by Panahbehagh et al. (2017), which relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, elements are ranked in sets based on linear extensions in partial order sets theory, where based on all the variables simultaneously. Results will be evaluated by some simulations and two real case study on economical, medicinal use of flowers and the pollution of herb-layer by Lead, Cadmium, Zinc and Sulfur in regions in the southwest of Germany.
{"title":"Sampling of Multiple Variables Based on Partially Ordered Set Theory","authors":"Bardia Panahbehagh, R. Bruggemann","doi":"10.52547/jirss.20.1.307","DOIUrl":"https://doi.org/10.52547/jirss.20.1.307","url":null,"abstract":"This paper is going to introduce a new method for ranked set sampling with multiple criteria. The method is based on a version of ranked set sampling, introduced by Panahbehagh et al. (2017), which relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, elements are ranked in sets based on linear extensions in partial order sets theory, where based on all the variables simultaneously. Results will be evaluated by some simulations and two real case study on economical, medicinal use of flowers and the pollution of herb-layer by Lead, Cadmium, Zinc and Sulfur in regions in the southwest of Germany.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43224961","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, the problem of estimating unknown parameters of a generalized halfnormal distribution is considered under Type II progressive hybrid censoring which is a combination of Type II progressive and hybrid censoring schemes. We obtain maximum likelihood estimators of parameters and also construct asymptotic intervals using the observed Fisher information matrix. Further Bayes estimates are computed under the squared error loss function by applying different approximation methods. We also obtain prediction estimates and prediction intervals of censored observations. The performance of different methods is compared using Monte Carlo simulations and a real data set is analyzed for illustrative purposes.
{"title":"Parameter Estimation and Prediction for the Generalized Half Normal Distribution under Progressive Hybrid Censoring","authors":"Farha Sultana, Y. Tripathi, M. K. Rastogi","doi":"10.29252/JIRSS.18.1.191","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.191","url":null,"abstract":"In this paper, the problem of estimating unknown parameters of a generalized halfnormal distribution is considered under Type II progressive hybrid censoring which is a combination of Type II progressive and hybrid censoring schemes. We obtain maximum likelihood estimators of parameters and also construct asymptotic intervals using the observed Fisher information matrix. Further Bayes estimates are computed under the squared error loss function by applying different approximation methods. We also obtain prediction estimates and prediction intervals of censored observations. The performance of different methods is compared using Monte Carlo simulations and a real data set is analyzed for illustrative purposes.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44183810","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":"A Goodness of Fit Test For Normality Based on Balakrishnan-Sanghvi Information","authors":"M. Tavakoli, N. Arghami, M. Abbasnejad","doi":"10.29252/JIRSS.18.1.177","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.177","url":null,"abstract":"","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42255426","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}
Many distributions have been presented with bathtub-shaped failure rates for real-life data. A two-parameter distribution was defined by Chen (2000). This distribution can have a bathtub-shaped or increasing failure rate function. In this paper, we consider two bivariate models based on the proposed distribution by Chen and use the proposed methods of Marshall and Olkin (1967) in the bivariate case and Marshall and Olkin (1997) in the univariate case. In the second case, their method is generalized to the bivariate case and a new bivariate distribution is introduced. These new bivariate distributions have natural interpretations, and they can be applied in fatal shock models or in competing risks models. We call these new distributions as the bivariate Chen (BCH) distribution and bivariate Chen-geometric (BCHG) distribution, respectively. Moreover, the BCH can be obtained as a special case of the BCHG model. Then, the various properties of the new distributions are investigated. The BCHG distribution has five parameters and the maximum likelihood estimators cannot be obtained in a closed form. We suggest using an EM algorithm that is very easy to implement. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze two real data sets for illustrative purposes.
{"title":"Statistical Analysis of Bivariate Failure Time Data based on Bathtub-shaped Failure Rate Model","authors":"S. Shoaee","doi":"10.29252/JIRSS.18.1.53","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.53","url":null,"abstract":"Many distributions have been presented with bathtub-shaped failure rates for real-life data. A two-parameter distribution was defined by Chen (2000). This distribution can have a bathtub-shaped or increasing failure rate function. In this paper, we consider two bivariate models based on the proposed distribution by Chen and use the proposed methods of Marshall and Olkin (1967) in the bivariate case and Marshall and Olkin (1997) in the univariate case. In the second case, their method is generalized to the bivariate case and a new bivariate distribution is introduced. These new bivariate distributions have natural interpretations, and they can be applied in fatal shock models or in competing risks models. We call these new distributions as the bivariate Chen (BCH) distribution and bivariate Chen-geometric (BCHG) distribution, respectively. Moreover, the BCH can be obtained as a special case of the BCHG model. Then, the various properties of the new distributions are investigated. The BCHG distribution has five parameters and the maximum likelihood estimators cannot be obtained in a closed form. We suggest using an EM algorithm that is very easy to implement. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze two real data sets for illustrative purposes.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42128303","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, bivariate lifetime distributions are often used to model reliability and survival data. In this paper, we introduce a bivariate Burr III distribution, so that the marginals have Burr III distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms. We suggest to use the ECM algorithm to compute the maximum likelihood estimators of the unknown parameters. We report some simulation results and perform one data analysis for illustrative purposes.
{"title":"Estimating the Parameters of the Bivariate Burr Type III Distribution by EM Algorithm","authors":"افسانه زازرمی عزیزی, عبدالرضا سیاره","doi":"10.29252/JIRSS.18.1.133","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.133","url":null,"abstract":"In recent years, bivariate lifetime distributions are often used to model reliability and survival data. In this paper, we introduce a bivariate Burr III distribution, so that the marginals have Burr III distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms. We suggest to use the ECM algorithm to compute the maximum likelihood estimators of the unknown parameters. We report some simulation results and perform one data analysis for illustrative purposes.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45639351","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 study the problem of optimal allocation of insurance layers for a portfolio of i.i.d exponential risks. Using the first stochastic dominance criterion, we obtain an optimal allocation for the total retain risks faced by a policyholder. This result partially generalizes the known result in the literature for deductible as well as policy limit coverages.
{"title":"Optimal Allocation of Policy Layers for Exponential Risks","authors":"Masoud Amiri, Muhyiddin Izadi, Baha-Eldin Khaledi","doi":"10.29252/JIRSS.18.1.1","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.1","url":null,"abstract":"In this paper, we study the problem of optimal allocation of insurance layers for a portfolio of i.i.d exponential risks. Using the first stochastic dominance criterion, we obtain an optimal allocation for the total retain risks faced by a policyholder. This result partially generalizes the known result in the literature for deductible as well as policy limit coverages.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49549450","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 point estimation of the value of a parameter, especially when the estimator under consideration has a probability density function, then the limit that the expected value of the estimator actually equaled the value of the parameter being estimated will tend towards zero for the estimator to be asymptotically unbiased. Hence, some interval about a point estimate needs to be included to accommodate for the region of an unbiased estimate. But in several occurrences when the random variable is not normally distributed as is common in practice; then the interval estimated for the location and scale parameters may be too wide to give the desired assurance. In this study, we have obtained some results on the confidence procedure for the location and scale parameters for symmetric and asymmetric exponential power distribution which is robust in the case of skewness or cases alike: tail heavier; and or thinner than the normal distribution using pivotal quantities approach, and on the basis of a random sample of fixed size n. Some simulation studies and applications are also examined.
{"title":"Interval Estimation for Symmetric and Asymmetric Exponential Power Distribution Parameters","authors":"A. Olósundé, A. T. Sóyínká","doi":"10.29252/JIRSS.18.1.237","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.237","url":null,"abstract":"In point estimation of the value of a parameter, especially when the estimator under consideration has a probability density function, then the limit that the expected value of the estimator actually equaled the value of the parameter being estimated will tend towards zero for the estimator to be asymptotically unbiased. Hence, some interval about a point estimate needs to be included to accommodate for the region of an unbiased estimate. But in several occurrences when the random variable is not normally distributed as is common in practice; then the interval estimated for the location and scale parameters may be too wide to give the desired assurance. In this study, we have obtained some results on the confidence procedure for the location and scale parameters for symmetric and asymmetric exponential power distribution which is robust in the case of skewness or cases alike: tail heavier; and or thinner than the normal distribution using pivotal quantities approach, and on the basis of a random sample of fixed size n. Some simulation studies and applications are also examined.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49472124","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}
Vahid Rezaei Tabar, Hosna Fathipor, Horacio Pérez-Sánchez, F. Eskandari, D. Plewczyński
. Hidden Markov models (HMM) are a ubiquitous tool for modeling time series data. The HMM can be poor at capturing dependency between observations because of the statistical assumptions it makes. Therefore, the extension of the HMM called forward-directed Autoregressive HMM (ARHMM) is considered to handle the dependencies between observations. It is also more appropriate to use an Autoregressive Hidden Markov Model directed backward in time. In this paper, we present a sequence-level mixture of these two forms of ARHMM (called MARHMM), e (cid:11) ectively allowing the model to choose for itself whether a forward-directed or backward-directed model or a soft combination of the two models are most appropriate for a given data set. For this purpose, we use the conditional independence relations in the context of a Bayesian network which is a probabilistic graphical model. The performance of the MARHMM is discussed by applying it to the simulated and real data sets. We show that the proposed model has greater modeling power than the conventional forward-directed ARHMM. The source code is available at https: // bitbucket.org 4dnucleome .
{"title":"Mixture of Forward-Directed and Backward-Directed Autoregressive Hidden Markov Models for Time series Modeling","authors":"Vahid Rezaei Tabar, Hosna Fathipor, Horacio Pérez-Sánchez, F. Eskandari, D. Plewczyński","doi":"10.29252/JIRSS.18.1.89","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.89","url":null,"abstract":". Hidden Markov models (HMM) are a ubiquitous tool for modeling time series data. The HMM can be poor at capturing dependency between observations because of the statistical assumptions it makes. Therefore, the extension of the HMM called forward-directed Autoregressive HMM (ARHMM) is considered to handle the dependencies between observations. It is also more appropriate to use an Autoregressive Hidden Markov Model directed backward in time. In this paper, we present a sequence-level mixture of these two forms of ARHMM (called MARHMM), e (cid:11) ectively allowing the model to choose for itself whether a forward-directed or backward-directed model or a soft combination of the two models are most appropriate for a given data set. For this purpose, we use the conditional independence relations in the context of a Bayesian network which is a probabilistic graphical model. The performance of the MARHMM is discussed by applying it to the simulated and real data sets. We show that the proposed model has greater modeling power than the conventional forward-directed ARHMM. The source code is available at https: // bitbucket.org 4dnucleome .","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47384534","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}
When a series of stochastic restrictions are available, we study the performance of the preliminary test generalized Liu estimators (PTGLEs) based on the Wald, likelihood ratio and Lagrangian multiplier tests. In this respect, the optimal range of the biasing parameter is obtained under the mean square error sense. For this, the minimum/maximum value of the biasing matrix components is used to give the proper optimal range, where the biasing matrix is D = diag(d1, d2, . . . , dp), 0 < di < 1, i = 1, . . . , p. We support our findings by some numerical illustrations.
在存在一系列随机约束条件的情况下，研究了基于Wald、似然比和拉格朗日乘子检验的初步检验广义Liu估计的性能。在均方误差意义下，得到了偏置参数的最优范围。为此，使用偏置矩阵分量的最小/最大值来给出适当的最优范围，其中偏置矩阵为D = diag(d1, d2，…)。， dp)， 0 < di < 1, I = 1，…我们用一些数值实例来支持我们的发现。
{"title":"On the Preliminary Test Generalized Liu Estimator with Series of Stochastic Restrictions","authors":"M. Karbalaee, S. M. M. Tabatabaey, M. Arashi","doi":"10.29252/JIRSS.18.1.113","DOIUrl":"https://doi.org/10.29252/JIRSS.18.1.113","url":null,"abstract":"When a series of stochastic restrictions are available, we study the performance of the preliminary test generalized Liu estimators (PTGLEs) based on the Wald, likelihood ratio and Lagrangian multiplier tests. In this respect, the optimal range of the biasing parameter is obtained under the mean square error sense. For this, the minimum/maximum value of the biasing matrix components is used to give the proper optimal range, where the biasing matrix is D = diag(d1, d2, . . . , dp), 0 < di < 1, i = 1, . . . , p. We support our findings by some numerical illustrations.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41529887","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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