Pub Date : 2021-02-01DOI: 10.2991/JSTA.D.210203.001
B. El-Desouky, R. Gomaa, A. Magar
{"title":"New Discrete Lifetime Distribution with Applications to Count Data","authors":"B. El-Desouky, R. Gomaa, A. Magar","doi":"10.2991/JSTA.D.210203.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210203.001","url":null,"abstract":"","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79805568","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 : 2021-02-01DOI: 10.2991/JSTA.D.210126.003
B. K. Pradhan, P. Dash, Upasana
AMS Subject Classification: 62M99, 60J80, 60J27, 60G07. Lineargrowth process with immigration and emigration is the general model in the study of population in biological and ecological systems, and their transient analysis is the most important factor in the understanding of the structural behavior of such systems. The probability-generating function π(z, t) of the probability distribution {pn(t)} of the random variable N(t) in many queuing situations concerning Birth, Death, Immigration, and Emigration were studied and we find the generalization of the transient solutions of the queuing systems and also studied its particular cases.
{"title":"A Note on Generalization of the Simplest Time-Dependent Discrete Markov Process: Linear Growth Process With Immigration-Emigration","authors":"B. K. Pradhan, P. Dash, Upasana","doi":"10.2991/JSTA.D.210126.003","DOIUrl":"https://doi.org/10.2991/JSTA.D.210126.003","url":null,"abstract":"AMS Subject Classification: 62M99, 60J80, 60J27, 60G07. Lineargrowth process with immigration and emigration is the general model in the study of population in biological and ecological systems, and their transient analysis is the most important factor in the understanding of the structural behavior of such systems. The probability-generating function π(z, t) of the probability distribution {pn(t)} of the random variable N(t) in many queuing situations concerning Birth, Death, Immigration, and Emigration were studied and we find the generalization of the transient solutions of the queuing systems and also studied its particular cases.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85828251","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 : 2021-02-01DOI: 10.2991/JSTA.D.210126.001
Azam Sabbaghi, F. Eskandari, Hamid Reza Navabpoor
In this paper, we are concerned with a robustifying high-dimensional (RHD) structured estimation in finite mixture of multinomial models. This method has been used in many applications that often involve outliers and data corruption. Thus, we introduce a class of the multinomial logistic mixture models for dependent variables having two or more discrete categorical levels. Through the optimization with the expectation maximization (EM) algorithm, we study two distinct ways to overcome sparsity in finite mixture of the multinomial logistic model; i.e., in the parameter space, or in the output space. It is shown that the new method is consistent for RHD structured estimation. Finally, we will implement the proposed method on real data.
{"title":"A Robust High-Dimensional Estimation of Multinomial Mixture Models","authors":"Azam Sabbaghi, F. Eskandari, Hamid Reza Navabpoor","doi":"10.2991/JSTA.D.210126.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210126.001","url":null,"abstract":"In this paper, we are concerned with a robustifying high-dimensional (RHD) structured estimation in finite mixture of multinomial models. This method has been used in many applications that often involve outliers and data corruption. Thus, we introduce a class of the multinomial logistic mixture models for dependent variables having two or more discrete categorical levels. Through the optimization with the expectation maximization (EM) algorithm, we study two distinct ways to overcome sparsity in finite mixture of the multinomial logistic model; i.e., in the parameter space, or in the output space. It is shown that the new method is consistent for RHD structured estimation. Finally, we will implement the proposed method on real data.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"28 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84709391","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 : 2021-02-01DOI: 10.2991/JSTA.D.210126.002
Omid Akhgari, M. Golalizadeh
Sometimes, invoking a single causal relationship to explain dependency between variables might not be appropriate particularly in some economic problems. Instead, two jointly related equations, where one of the explanatory variables is endogenous, can represent the actual inheritance inter-relationship among variables. Such typical models are called simultaneous equation models of which the seemingly unrelated regression (SUR) models is a special case. Substantial progress has been made regarding the statistical inference on estimating the parameters of these models in which errors follow a normal distribution. But, less research was devoted to a case that the distributions of the errors are asymmetric. In this paper, statistical inference on the parameters for the SUR models, assuming the skew-normal density for errors, is tackled. Moreover, the results of the study are compared with those of other naive methodologies. The proposed model is utilized to analyze the income and expenditure of Iranian rural households in the year 2009.
{"title":"On Seemingly Unrelated Regression Model with Skew Error","authors":"Omid Akhgari, M. Golalizadeh","doi":"10.2991/JSTA.D.210126.002","DOIUrl":"https://doi.org/10.2991/JSTA.D.210126.002","url":null,"abstract":"Sometimes, invoking a single causal relationship to explain dependency between variables might not be appropriate particularly in some economic problems. Instead, two jointly related equations, where one of the explanatory variables is endogenous, can represent the actual inheritance inter-relationship among variables. Such typical models are called simultaneous equation models of which the seemingly unrelated regression (SUR) models is a special case. Substantial progress has been made regarding the statistical inference on estimating the parameters of these models in which errors follow a normal distribution. But, less research was devoted to a case that the distributions of the errors are asymmetric. In this paper, statistical inference on the parameters for the SUR models, assuming the skew-normal density for errors, is tackled. Moreover, the results of the study are compared with those of other naive methodologies. The proposed model is utilized to analyze the income and expenditure of Iranian rural households in the year 2009.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"2010 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86296110","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 : 2021-02-01DOI: 10.2991/JSTA.D.210121.001
Mahdieh Bayati, S. K. Ghoreishi, Jingjing Wu
In this paper, we first illustrate the restricted empirical likelihood function, as an alternative to the usual empirical likelihood. Then, we use this quasi-empirical likelihood function as a basis for Bayesian analysis of AR(r) time series models. The efficiency of both the posterior computation algorithm, when the estimating equations are linear functions of the parameters, and the EM algorithm for estimating hyper-parameters is an appealing property of our proposed approach. Moreover, the competitive finitesample performance of this proposed method is illustrated via both simulation study and analysis of a real dataset.
{"title":"Restricted Empirical Likelihood Estimation for Time Series Autoregressive Models","authors":"Mahdieh Bayati, S. K. Ghoreishi, Jingjing Wu","doi":"10.2991/JSTA.D.210121.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210121.001","url":null,"abstract":"In this paper, we first illustrate the restricted empirical likelihood function, as an alternative to the usual empirical likelihood. Then, we use this quasi-empirical likelihood function as a basis for Bayesian analysis of AR(r) time series models. The efficiency of both the posterior computation algorithm, when the estimating equations are linear functions of the parameters, and the EM algorithm for estimating hyper-parameters is an appealing property of our proposed approach. Moreover, the competitive finitesample performance of this proposed method is illustrated via both simulation study and analysis of a real dataset.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77823101","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 : 2021-02-01DOI: 10.2991/JSTA.D.210201.001
Kirti Arekar, Rinku Jain, Surender Kumar
This paper discusses the problem of how Monte-Carlo simulation method is deal with Bayesian estimation of reliability of system of n s-independent two-state component. Time-to-failure for each component is assumed to have Weibull distribution with different parameters for each component. The shape parameter for each component is assumed to be known with the scale parameter distributed with a priori Rayleigh distribution with known parameters. Monte-Carlo simulation is used to generate the random deviates for the scale parameters and replicates for time-to-failure for each combination of scale parameters values are generated. Reliability is estimated as a function of time. Further, for the Bayes estimation of reliability we assume Poisson distribution with a priori time-shifted Rayleigh distribution. Finally, the robustness in the Bayesian estimation problem relative to changes in the assigned priori distribution is considered. We approximate the Bayes estimator of the reliability. The Bayes risk with respect to the priori time-shifted beta distribution is considered and at last approximate robustness of the Bayes estimator of reliability is examined with respect to the uniform priori. We have compared the maximum likelihood estimator of reliability with the Bayes estimator with prior uniform distribution. Finally, the method is illustrated by considering the illustrative example of vehicle system.
{"title":"Bayesian Estimation of System Reliability Models Using Monte-Carlo Technique of Simulation","authors":"Kirti Arekar, Rinku Jain, Surender Kumar","doi":"10.2991/JSTA.D.210201.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210201.001","url":null,"abstract":"This paper discusses the problem of how Monte-Carlo simulation method is deal with Bayesian estimation of reliability of system of n s-independent two-state component. Time-to-failure for each component is assumed to have Weibull distribution with different parameters for each component. The shape parameter for each component is assumed to be known with the scale parameter distributed with a priori Rayleigh distribution with known parameters. Monte-Carlo simulation is used to generate the random deviates for the scale parameters and replicates for time-to-failure for each combination of scale parameters values are generated. Reliability is estimated as a function of time. Further, for the Bayes estimation of reliability we assume Poisson distribution with a priori time-shifted Rayleigh distribution. Finally, the robustness in the Bayesian estimation problem relative to changes in the assigned priori distribution is considered. We approximate the Bayes estimator of the reliability. The Bayes risk with respect to the priori time-shifted beta distribution is considered and at last approximate robustness of the Bayes estimator of reliability is examined with respect to the uniform priori. We have compared the maximum likelihood estimator of reliability with the Bayes estimator with prior uniform distribution. Finally, the method is illustrated by considering the illustrative example of vehicle system.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"643 1","pages":"149-163"},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74732033","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 : 2021-02-01DOI: 10.2991/JSTA.D.210129.001
Muhammad Ali, Haseeb Athar
This study introduces generalized transmuted family of distributions. We investigate the special cases of our generalized transmuted distribution to match with some other generalization available in literature. The transmuted distributions are applied to Weibull distribution to find generalized rank map transmuted Weibull distribution. The distributional characteristics such as probability curve, mean, variance, skewness, kurtosis, distribution of largest order statistics, and their characteristics studied to compare with ordinary Weibull distribution. Hazard rate functions and distributional characteristics of largest order statistics of transmuted distributions are also studied. It is observed that the transmuted distributions are more flexible to model real data, since the data can present a high degree of skewness and kurtosis. If someone is interested to locate more flexible and higher degree of skewed distribution can explore this generalized transmuted family of distributions for future use.
{"title":"Generalized Rank Mapped Transmuted Distribution for Generating Families of Continuous Distributions","authors":"Muhammad Ali, Haseeb Athar","doi":"10.2991/JSTA.D.210129.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210129.001","url":null,"abstract":"This study introduces generalized transmuted family of distributions. We investigate the special cases of our generalized transmuted distribution to match with some other generalization available in literature. The transmuted distributions are applied to Weibull distribution to find generalized rank map transmuted Weibull distribution. The distributional characteristics such as probability curve, mean, variance, skewness, kurtosis, distribution of largest order statistics, and their characteristics studied to compare with ordinary Weibull distribution. Hazard rate functions and distributional characteristics of largest order statistics of transmuted distributions are also studied. It is observed that the transmuted distributions are more flexible to model real data, since the data can present a high degree of skewness and kurtosis. If someone is interested to locate more flexible and higher degree of skewed distribution can explore this generalized transmuted family of distributions for future use.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"34 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88042186","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 : 2021-01-01DOI: 10.2991/jsta.d.201230.001
R. Vijayaragunathan, M. R. Srinivasan
Inthetraditionaltwo-wayanalysisofvariance(ANOVA)model,itispossibletoidentifythesignificanceofboththemaineffects andtheirinteractionbasedonthe P values. However, it is not possible to determine how much data supports the model when these effects are incorporated into the model. To overcome this practical difficulty, we applied Bayes factors for hierarchical models to check the intensity of the effects (both main and interaction). The objective is to identify the impact of the main and interaction effects based on a comparison of Bayes factors of the hierarchical ANOVA models. The application of Bayes factors enables to observe which model strengthens more while including or eliminating the effects in the model. Consequently, this paper proposes three priors such as Zellner’s g , Jefferys-Zellner-Siow, and Hyper-g priors, to compute the Bayes factor. Finally, we extended this procedure to the simulation data for the generalization of the Bayesian results.
{"title":"Bayes Factors for Comparison of Two-Way ANOVA Models","authors":"R. Vijayaragunathan, M. R. Srinivasan","doi":"10.2991/jsta.d.201230.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201230.001","url":null,"abstract":"Inthetraditionaltwo-wayanalysisofvariance(ANOVA)model,itispossibletoidentifythesignificanceofboththemaineffects andtheirinteractionbasedonthe P values. However, it is not possible to determine how much data supports the model when these effects are incorporated into the model. To overcome this practical difficulty, we applied Bayes factors for hierarchical models to check the intensity of the effects (both main and interaction). The objective is to identify the impact of the main and interaction effects based on a comparison of Bayes factors of the hierarchical ANOVA models. The application of Bayes factors enables to observe which model strengthens more while including or eliminating the effects in the model. Consequently, this paper proposes three priors such as Zellner’s g , Jefferys-Zellner-Siow, and Hyper-g priors, to compute the Bayes factor. Finally, we extended this procedure to the simulation data for the generalization of the Bayesian results.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"289 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83435232","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 : 2021-01-01DOI: 10.2991/JSTA.D.210111.001
M. M. Saber, A. Nematollahi, M. Mohammadzadeh
Earlier works on spatial prediction issue often assume that the spatial data are realization of Gaussian random field. However, this assumption is not applicable to the skewed and kurtosis distributed data. The closed skew normal distribution has been used in these circumstances. As another alternative, we apply generalized skew Laplace distributions for defining a skew and heavy tailed random field for Bayesian prediction. Simulation study and a real problem are then applied to evaluate the performance of this model.
{"title":"Generalized Skew Laplace Random Fields: Bayesian Spatial Prediction for Skew and Heavy Tailed Data","authors":"M. M. Saber, A. Nematollahi, M. Mohammadzadeh","doi":"10.2991/JSTA.D.210111.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210111.001","url":null,"abstract":"Earlier works on spatial prediction issue often assume that the spatial data are realization of Gaussian random field. However, this assumption is not applicable to the skewed and kurtosis distributed data. The closed skew normal distribution has been used in these circumstances. As another alternative, we apply generalized skew Laplace distributions for defining a skew and heavy tailed random field for Bayesian prediction. Simulation study and a real problem are then applied to evaluate the performance of this model.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"30 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77863638","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 : 2021-01-01DOI: 10.2991/JSTA.D.210107.001
B. K. Gupt, Md. Irphan Ahamed
This paper considers the problem of optimum stratification for a model-based allocation under a superpopulation model. The equations giving optimum points of stratification have been derived and a few methods for finding approximately optimum points of stratification have been obtained from the equations. Numerical illustrations using generated data have been worked out and the proposed methods of stratification have been compared with equal interval stratification.
{"title":"Construction of Strata for a Model-Based Allocation Under a Superpopulation Model","authors":"B. K. Gupt, Md. Irphan Ahamed","doi":"10.2991/JSTA.D.210107.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210107.001","url":null,"abstract":"This paper considers the problem of optimum stratification for a model-based allocation under a superpopulation model. The equations giving optimum points of stratification have been derived and a few methods for finding approximately optimum points of stratification have been obtained from the equations. Numerical illustrations using generated data have been worked out and the proposed methods of stratification have been compared with equal interval stratification.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"420 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75874579","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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