SeyedReza HosseiniShojaei, Y. Waghei, M. Mohammadzadeh
. Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that random effects have Gaussian distribution, but the assumption is questionable. This assumption is replaced in the present work, using a skew Gaussian distribution for the latent variables, which is more flexible and includes Gaussian distribution. We examine the proposed method using a real discrete data set.
{"title":"Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation","authors":"SeyedReza HosseiniShojaei, Y. Waghei, M. Mohammadzadeh","doi":"10.29252/JSRI.14.2.157","DOIUrl":"https://doi.org/10.29252/JSRI.14.2.157","url":null,"abstract":". Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that random effects have Gaussian distribution, but the assumption is questionable. This assumption is replaced in the present work, using a skew Gaussian distribution for the latent variables, which is more flexible and includes Gaussian distribution. We examine the proposed method using a real discrete data set.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124857652","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, a new generalization of the half-normal distribution which is called the perturbed half-normal distribution is introduced. The new distribution belongs to a family of distributions which includes the half-normal distribution along with an extra parameter to regulate skewness. The probability density function (pdf) is derived and some various properties of the new distribution are obtained. The derived properties include the cumulative distribution function (cdf), the r th moment, moment generating function, characteristic function, mean deviation about the mean and estimation of the parameters using the method of moments and maximum likelihood. Finally, the flexibility and potentiality of the new distribution is illustrated in an application to two real data sets.
{"title":"A Perturbed Half-normal Distribution and Its Applications","authors":"E. Mahmoudi, R. Lalehzari, R. Meshkat","doi":"10.29252/jsri.14.2.219","DOIUrl":"https://doi.org/10.29252/jsri.14.2.219","url":null,"abstract":". In this paper, a new generalization of the half-normal distribution which is called the perturbed half-normal distribution is introduced. The new distribution belongs to a family of distributions which includes the half-normal distribution along with an extra parameter to regulate skewness. The probability density function (pdf) is derived and some various properties of the new distribution are obtained. The derived properties include the cumulative distribution function (cdf), the r th moment, moment generating function, characteristic function, mean deviation about the mean and estimation of the parameters using the method of moments and maximum likelihood. Finally, the flexibility and potentiality of the new distribution is illustrated in an application to two real data sets.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133757214","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 propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.
{"title":"Rank based Least-squares Independent Component Analysis","authors":"Jafar Rahmanishamsi, A. Dolati","doi":"10.29252/JSRI.14.2.247","DOIUrl":"https://doi.org/10.29252/JSRI.14.2.247","url":null,"abstract":". In this paper, we propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"489 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129847914","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, it is assumed that the mean of a normal process is monitored by a CUSUM control chart. When the control chart triggers a signal and declares that the process has gone out of control, a search process is started to find the time of change and the causes of going the process out of control. Several methods (plans) for finding the true (real) change point is proposed. It is shown that the plans which are based on the likelihood of the points in time perform better.
{"title":"Finding True Change Point When a CUSUM Control Chart is Used","authors":"M. E. D. Monfared, Fazlollah Lak","doi":"10.29252/JSRI.15.1.99","DOIUrl":"https://doi.org/10.29252/JSRI.15.1.99","url":null,"abstract":"In this paper, it is assumed that the mean of a normal process is monitored by a CUSUM control chart. When the control chart triggers a signal and declares that the process has gone out of control, a search process is started to find the time of change and the causes of going the process out of control. Several methods (plans) for finding the true (real) change point is proposed. It is shown that the plans which are based on the likelihood of the points in time perform better.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"248 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117341241","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}
H. Yousof, M. Majumder, S. M. A. Jahanshahi, M. M. Ali, G. Hamedani
We propose a new class of continuous models called the Weibull Generalized G family with two extra positive shape parameters, which extends several well-known models. We obtain some of its mathematical properties including ordinary and incomplete moments, generating function, order statistics, probability weighted moments, entropies, residual, and reversed residual life functions. Characterizations based on a ratio of two truncated moments, in terms of hazard function and based on certain functions of the random variable are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. The usefulness of the proposed models is illustrated via three real data sets.
{"title":"A New Weibull Class of Distributions: Theory, Characterizations and Applications","authors":"H. Yousof, M. Majumder, S. M. A. Jahanshahi, M. M. Ali, G. Hamedani","doi":"10.29252/jsri.15.1.45","DOIUrl":"https://doi.org/10.29252/jsri.15.1.45","url":null,"abstract":"We propose a new class of continuous models called the Weibull Generalized G family with two extra positive shape parameters, which extends several well-known models. We obtain some of its mathematical properties including ordinary and incomplete moments, generating function, order statistics, probability weighted moments, entropies, residual, and reversed residual life functions. Characterizations based on a ratio of two truncated moments, in terms of hazard function and based on certain functions of the random variable are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. The usefulness of the proposed models is illustrated via three real data sets.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116296529","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}
. Shirakura et al. (1996) has been introduced and calculated the search probability ( SP ) for normal search model. However, in practical situations the normality assumption may fail. In this study, we consider a more realistic underlying skew-normal/independent ( SNI ) model and obtain the SP . This is a general case, in a sense that the result in Shirakura et al. (1996) is its special case. The proposed SP carries some reliable properties and can be used as a design comparison criterion to compare and rank the search designs ( SD ).
。Shirakura et al.(1996)已经引入并计算了正常搜索模型的搜索概率(SP)。然而，在实际情况下，正态性假设可能会失败。在本研究中，我们考虑了一个更现实的潜在斜正态/独立(SNI)模型，并获得了SP。这是一般情况，从某种意义上说，Shirakura et al.(1996)的结果是它的特殊情况。该方法具有一定的可靠性，可作为设计比较标准，对搜索设计进行比较和排序。
{"title":"Search Probability for Non-zero Effects Detection under Skew-Normal/Independent Search Model","authors":"S. Sadeghi, H. Talebi","doi":"10.29252/jsri.15.1.147","DOIUrl":"https://doi.org/10.29252/jsri.15.1.147","url":null,"abstract":". Shirakura et al. (1996) has been introduced and calculated the search probability ( SP ) for normal search model. However, in practical situations the normality assumption may fail. In this study, we consider a more realistic underlying skew-normal/independent ( SNI ) model and obtain the SP . This is a general case, in a sense that the result in Shirakura et al. (1996) is its special case. The proposed SP carries some reliable properties and can be used as a design comparison criterion to compare and rank the search designs ( SD ).","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116609757","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}
. A proper method of monitoring a stochastic system is to utilize the control charts of statistical process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts, an assumption is made that there is no correlation within the samples. However, in practice, there are many industrial cases in which the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Although some research works have been done on the economic design of control charts with single assignable cause with correlated data, the economic statistical design of X control chart for correlated data under Weibull shock model with modified Taguchi loss function have not been presented yet. Using modified Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and different combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost mod-* els under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling has a lower cost than that with uniform sampling. MSC 2010: 62P30.
{"title":"Constrained Optimal Design of $bar{X}$ Control Chart for Correlated Data under Weibull Shock Model with Multiple Assignable Causes and Taguchi Loss Function","authors":"M. H. Naderi, A. Seif, M. B. Moghadam","doi":"10.29252/JSRI.15.1.1","DOIUrl":"https://doi.org/10.29252/JSRI.15.1.1","url":null,"abstract":". A proper method of monitoring a stochastic system is to utilize the control charts of statistical process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts, an assumption is made that there is no correlation within the samples. However, in practice, there are many industrial cases in which the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Although some research works have been done on the economic design of control charts with single assignable cause with correlated data, the economic statistical design of X control chart for correlated data under Weibull shock model with modified Taguchi loss function have not been presented yet. Using modified Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and different combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost mod-* els under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling has a lower cost than that with uniform sampling. MSC 2010: 62P30.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124429438","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 Tsallis relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the Tsallis relative entropy between two finite subsequences of above mentioned chains with the help of the definition of Tsallis relative entropy between two random variables then we define the Tsallis relative entropy rate between these stochastic processes. Finally, we calculate Tsallis relative entropy rate for some hidden Markov models.
{"title":"On Tsallis Relative Entropy Rate of Hidden Markov Models","authors":"Z. Nikooravesh","doi":"10.29252/JSRI.15.1.83","DOIUrl":"https://doi.org/10.29252/JSRI.15.1.83","url":null,"abstract":"In this paper we study the Tsallis relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the Tsallis relative entropy between two finite subsequences of above mentioned chains with the help of the definition of Tsallis relative entropy between two random variables then we define the Tsallis relative entropy rate between these stochastic processes. Finally, we calculate Tsallis relative entropy rate for some hidden Markov models.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132663127","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}
A new generalized version of the mixed Poisson distribution, called the Poisson-beta exponential (PBE) distribution, is obtained by mixing the Poisson and the beta exponential (BE) distributions. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE distribution to data, and the fit model is compared with that obtained using other distributions.
{"title":"Poisson-Beta Exponential Distribution: Properties and Applications","authors":"E. Mahmoudi, Hossein Zamani, R. Meshkat","doi":"10.29252/jsri.15.1.119","DOIUrl":"https://doi.org/10.29252/jsri.15.1.119","url":null,"abstract":"A new generalized version of the mixed Poisson distribution, called the Poisson-beta exponential (PBE) distribution, is obtained by mixing the Poisson and the beta exponential (BE) distributions. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE distribution to data, and the fit model is compared with that obtained using other distributions.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130626887","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 presents exact joint confidence regions for the parameters of the Rayleigh distribution based on record data. By providing some appropriate pivotal quantities, we construct several joint confidence regions for the Rayleigh parameters. These joint confidence regions are useful for constructing confidence regions for functions of the unknown parameters. Applications of the joint confidence regions using two environmental data sets are presented for illustrative purposes. Finally, a simulation study is conducted to study the performance of the proposed joint confidence regions.
{"title":"Rayleigh Confidence Regions based on Record Data","authors":"M. Abdi, A. Asgharzadeh","doi":"10.29252/JSRI.14.2.171","DOIUrl":"https://doi.org/10.29252/JSRI.14.2.171","url":null,"abstract":". This paper presents exact joint confidence regions for the parameters of the Rayleigh distribution based on record data. By providing some appropriate pivotal quantities, we construct several joint confidence regions for the Rayleigh parameters. These joint confidence regions are useful for constructing confidence regions for functions of the unknown parameters. Applications of the joint confidence regions using two environmental data sets are presented for illustrative purposes. Finally, a simulation study is conducted to study the performance of the proposed joint confidence regions.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120964410","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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