Pub Date : 2017-03-15DOI: 10.18869/acadpub.jsri.13.2.231
Abbas Mahdavi, G. O. Silva
A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochastic orders, order statistics and some entropies are discussed. Maximum likelihood method is used to estimate the unknown parameters and the Fisher information matrix is given. The obtained results are validated using a real data set and it is shown that the new family provides a better fit than some other known distributions.
{"title":"A Method to Expand Family of Continuous Distributions based on Truncated Distributions","authors":"Abbas Mahdavi, G. O. Silva","doi":"10.18869/acadpub.jsri.13.2.231","DOIUrl":"https://doi.org/10.18869/acadpub.jsri.13.2.231","url":null,"abstract":"A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochastic orders, order statistics and some entropies are discussed. Maximum likelihood method is used to estimate the unknown parameters and the Fisher information matrix is given. The obtained results are validated using a real data set and it is shown that the new family provides a better fit than some other known distributions.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114948573","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 : 2017-03-10DOI: 10.18869/ACADPUB.JSRI.13.2.181
Gholamhossein Gholami
The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG’s parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution. As the posterior distributions do not admit a closed form, we do an approximated inference by using Gibbs and Metropolis-Hastings algorithm.
{"title":"Bayesian Estimation of Parameters in the Exponentiated Gumbel Distribution","authors":"Gholamhossein Gholami","doi":"10.18869/ACADPUB.JSRI.13.2.181","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.13.2.181","url":null,"abstract":"The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG’s parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution. As the posterior distributions do not admit a closed form, we do an approximated inference by using Gibbs and Metropolis-Hastings algorithm.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130293494","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 : 2016-09-15DOI: 10.18869/acadpub.jsri.13.1.6
Esmail Dehghan Monfared, Fazlollah Lak
The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly find the starting time or the change point of a process disturbance. To do this, after a control chart triggers an out-of-control signal, an order of points in time (known as a plan) should be identified such that if the process examined sequentially at them, the true change point is detected as soon as possible. A typical method is to start the examination of the process from the signal time of the control chart and proceed to neighbouring points. In this paper, we establish a Bayesian method to solve this problem, i.e. to find a plan for examining the process sequentially such that it minimizes the Bayes risk among all other possible plans. At last, our proposed Bayes method is applied to a normal process, and compared to a typical method which is usually used to find the true change point through a series of simulations.
{"title":"Bayesian Method for Finding True Change Point when a Control Chart is used","authors":"Esmail Dehghan Monfared, Fazlollah Lak","doi":"10.18869/acadpub.jsri.13.1.6","DOIUrl":"https://doi.org/10.18869/acadpub.jsri.13.1.6","url":null,"abstract":"The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly find the starting time or the change point of a process disturbance. To do this, after a control chart triggers an out-of-control signal, an order of points in time (known as a plan) should be identified such that if the process examined sequentially at them, the true change point is detected as soon as possible. A typical method is to start the examination of the process from the signal time of the control chart and proceed to neighbouring points. In this paper, we establish a Bayesian method to solve this problem, i.e. to find a plan for examining the process sequentially such that it minimizes the Bayes risk among all other possible plans. At last, our proposed Bayes method is applied to a normal process, and compared to a typical method which is usually used to find the true change point through a series of simulations.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127005636","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 : 2016-09-15DOI: 10.18869/ACADPUB.JSRI.13.1.5
M. Mirjalili, H. Torabi, H. Nadeb
This paper considers the estimation of the stress-strength parameter, say R, based on two independent Type-I progressively hybrid censored samples from exponential populations with different parameters. The maximum likelihood estimator and asymptotic confidence interval for R are obtained. Bayes estimator of R is also derived under the assumption of independent gamma priors. A Monte Carlo simulation study is used to evaluate the performance of maximum likelihood estimator, Bayes estimator and asymptotic confidence interval. Finally, a pair of real data sets is analyzed for illustrative purposes.
{"title":"Stress-strength Reliability of Exponential Distribution based on Type-I Progressively Hybrid Censored Samples","authors":"M. Mirjalili, H. Torabi, H. Nadeb","doi":"10.18869/ACADPUB.JSRI.13.1.5","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.13.1.5","url":null,"abstract":"This paper considers the estimation of the stress-strength parameter, say R, based on two independent Type-I progressively hybrid censored samples from exponential populations with different parameters. The maximum likelihood estimator and asymptotic confidence interval for R are obtained. Bayes estimator of R is also derived under the assumption of independent gamma priors. A Monte Carlo simulation study is used to evaluate the performance of maximum likelihood estimator, Bayes estimator and asymptotic confidence interval. Finally, a pair of real data sets is analyzed for illustrative purposes.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126639122","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 : 2016-09-15DOI: 10.18869/ACADPUB.JSRI.13.1.1
M. Safavinejad, S. Jomhoori, H. A. Noughabi
. In this paper, we first describe the skew-Laplace distribution and its properties. We then introduce a goodness of fit test for this distribution according to the density-based empirical likelihood ratio concept. Asymptotic consistency of the proposed test is demonstrated. The critical values and Type I error of the test are obtained by Monte Carlo simulations. More-over, the empirical distribution function (EDF) tests are considered for the skew-Laplace distribution to show they do not have acceptable Type I error in comparison with the proposed test. Results show that the proposed test has an excellent Type I error which does not depend on the unknown parameters. The results obtained from simulation studies designed to investigate the power of the test are presented, too. The applicability of the proposed test in practice is demonstrated by real data examples.
{"title":"Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach","authors":"M. Safavinejad, S. Jomhoori, H. A. Noughabi","doi":"10.18869/ACADPUB.JSRI.13.1.1","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.13.1.1","url":null,"abstract":". In this paper, we first describe the skew-Laplace distribution and its properties. We then introduce a goodness of fit test for this distribution according to the density-based empirical likelihood ratio concept. Asymptotic consistency of the proposed test is demonstrated. The critical values and Type I error of the test are obtained by Monte Carlo simulations. More-over, the empirical distribution function (EDF) tests are considered for the skew-Laplace distribution to show they do not have acceptable Type I error in comparison with the proposed test. Results show that the proposed test has an excellent Type I error which does not depend on the unknown parameters. The results obtained from simulation studies designed to investigate the power of the test are presented, too. The applicability of the proposed test in practice is demonstrated by real data examples.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125049368","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 : 2016-09-15DOI: 10.18869/acadpub.jsri.13.1.4
A. Sayyareh
Model selection aims to find the optimum model. A good model will generally yield good results. Herein lies the importance of model evaluation criteria for assessing the goodness of a subjective model. In this work we want to answer to this question that, how could infinite set of all possible models that could have given rise to data, be narrowed down to a reasonable set of statistical models? This paper considers a finite mixture of the known criterion to the model selection problem to answer to the question. The aim of this kind of criteria is to select an reasonable set of models based on a measure of closeness. We demonstrate that a very general class of statistical criterion, which we call that finite mixture Kullback-Leibler criterion, provides a way of rival theory model selection. In this work we have proposed two types of coefficients for the mixture criterion, one based on the density and another one based on the risk function. The simulation study and real data analysis confirme the proposed criteria.
{"title":"Admissible Set of Rival Models based on the Mixture of Kullback-Leibler Risks","authors":"A. Sayyareh","doi":"10.18869/acadpub.jsri.13.1.4","DOIUrl":"https://doi.org/10.18869/acadpub.jsri.13.1.4","url":null,"abstract":"Model selection aims to find the optimum model. A good model will generally yield good results. Herein lies the importance of model evaluation criteria for assessing the goodness of a subjective model. In this work we want to answer to this question that, how could infinite set of all possible models that could have given rise to data, be narrowed down to a reasonable set of statistical models? This paper considers a finite mixture of the known criterion to the model selection problem to answer to the question. The aim of this kind of criteria is to select an reasonable set of models based on a measure of closeness. We demonstrate that a very general class of statistical criterion, which we call that finite mixture Kullback-Leibler criterion, provides a way of rival theory model selection. In this work we have proposed two types of coefficients for the mixture criterion, one based on the density and another one based on the risk function. The simulation study and real data analysis confirme the proposed criteria.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134520720","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 : 2016-09-15DOI: 10.18869/ACADPUB.JSRI.13.1.2
S. Baratpour, A. Khammar
. Tsallis entropy and order statistics are important in engineering reliability, image and signal processing. In this paper, we try to extend the concept of Tsallis entropy using order statistics. For this purpose, we propose the Tsallis entropy of order statistics and for it we obtain upper and lower bounds and some results on stochastic comparisons.
{"title":"Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons","authors":"S. Baratpour, A. Khammar","doi":"10.18869/ACADPUB.JSRI.13.1.2","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.13.1.2","url":null,"abstract":". Tsallis entropy and order statistics are important in engineering reliability, image and signal processing. In this paper, we try to extend the concept of Tsallis entropy using order statistics. For this purpose, we propose the Tsallis entropy of order statistics and for it we obtain upper and lower bounds and some results on stochastic comparisons.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130480268","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 : 2016-03-15DOI: 10.18869/ACADPUB.JSRI.12.2.179
S. Ghafouri, A. H. Rad, M. Doostparast
Statistical prediction analysis plays an important role in a wide range of fields. Examples include engineering systems, design of experiments, etc. In this paper, based on progressively Type-II right censored data, Bayesian two-sample point and interval predictors are developed under both informative and non-informative priors. By assuming a generalized exponential model, prediction bounds as well as Bayes point predictors are obtained under the squared error loss (SEL) and the Linear-Exponential (LINEX) loss functions for the order statistic in a future progressively Type-II censored sample with an arbitrary progressive censoring scheme. The derived results may be used for prediction of total time on test in lifetime experiments. In addition to numerical method, Gibbs sampling procedure (as Markov Chain Monte Carlo method) are used to assess approximate prediction bounds and Bayes point predictors under the SEL and LINEX loss functions. The performance of the proposed prediction procedures are also demonstrated via a Monte Carlo simulation study and an illustrative example, for each method.
统计预测分析在广泛的领域中发挥着重要的作用。例子包括工程系统、实验设计等。本文基于渐进式ⅱ型右截尾数据，分别在信息先验和非信息先验条件下，建立了贝叶斯双样本点和区间预测模型。通过假设一个广义指数模型，对任意渐进删减方案的未来渐进式ii型删减样本，在平方误差损失(SEL)和线性指数损失(LINEX)函数下得到阶统计量的预测界和贝叶斯点预测量。所得结果可用于寿命试验中试验总时间的预测。除了数值方法外，Gibbs抽样过程(如Markov Chain Monte Carlo方法)用于评估SEL和LINEX损失函数下的近似预测界和Bayes点预测量。对于每种方法，所提出的预测程序的性能也通过蒙特卡罗模拟研究和说明性示例进行了验证。
{"title":"Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions","authors":"S. Ghafouri, A. H. Rad, M. Doostparast","doi":"10.18869/ACADPUB.JSRI.12.2.179","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.2.179","url":null,"abstract":"Statistical prediction analysis plays an important role in a wide range of fields. Examples include engineering systems, design of experiments, etc. In this paper, based on progressively Type-II right censored data, Bayesian two-sample point and interval predictors are developed under both informative and non-informative priors. By assuming a generalized exponential model, prediction bounds as well as Bayes point predictors are obtained under the squared error loss (SEL) and the Linear-Exponential (LINEX) loss functions for the order statistic in a future progressively Type-II censored sample with an arbitrary progressive censoring scheme. The derived results may be used for prediction of total time on test in lifetime experiments. In addition to numerical method, Gibbs sampling procedure (as Markov Chain Monte Carlo method) are used to assess approximate prediction bounds and Bayes point predictors under the SEL and LINEX loss functions. The performance of the proposed prediction procedures are also demonstrated via a Monte Carlo simulation study and an illustrative example, for each method.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128803528","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 : 2016-03-15DOI: 10.18869/ACADPUB.JSRI.12.2.205
V. Nekoukhou
In this paper, a discrete analog of the beta-Rayleigh distribution is studied. This new distribution contains the generalized discrete Rayleigh and discrete Rayleigh distributions as special sub-models. Some distributional and moment properties of the new discrete distribution as well as its order statistics are discussed. We will see that the hazard rate function of the new model can be increasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and, finally, the model with a real data set is examined.
{"title":"The Beta-Rayleigh Distribution on the Lattice of Integers","authors":"V. Nekoukhou","doi":"10.18869/ACADPUB.JSRI.12.2.205","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.2.205","url":null,"abstract":"In this paper, a discrete analog of the beta-Rayleigh distribution is studied. This new distribution contains the generalized discrete Rayleigh and discrete Rayleigh distributions as special sub-models. Some distributional and moment properties of the new discrete distribution as well as its order statistics are discussed. We will see that the hazard rate function of the new model can be increasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and, finally, the model with a real data set is examined.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115104099","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 : 2016-03-15DOI: 10.18869/acadpub.jsri.12.2.163
Z. Rahnamaei
One of the most interesting problems in distribution theory is constructing the distributions, which are appropriate for fitting skewed and heavy-tailed data sets. In this paper, we introduce a skew-slash distribution by using the scale mixture of the generalized gamma distribution. Some properties of this distribution are obtained. An EM-type algorithm is presented to estimate the parameters. Finally, we provide a simulation study and an application to real data to illustrate the modeling strength of the proposed distribution.
{"title":"The Location-Scale Mixture of Generalized Gamma Distribution: Estimation and Case Influence Diagnostics","authors":"Z. Rahnamaei","doi":"10.18869/acadpub.jsri.12.2.163","DOIUrl":"https://doi.org/10.18869/acadpub.jsri.12.2.163","url":null,"abstract":"One of the most interesting problems in distribution theory is constructing the distributions, which are appropriate for fitting skewed and heavy-tailed data sets. In this paper, we introduce a skew-slash distribution by using the scale mixture of the generalized gamma distribution. Some properties of this distribution are obtained. An EM-type algorithm is presented to estimate the parameters. Finally, we provide a simulation study and an application to real data to illustrate the modeling strength of the proposed distribution.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129392228","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：