Pub Date : 2016-03-15DOI: 10.18869/ACADPUB.JSRI.12.2.225
M. N. Qomi, L. Barmoodeh
In the present paper, we study shrinkage testimation for the unknown scale parameter θ > 0 of the exponential distribution based on record data under the asymmetric squared log error loss function. A minimum risk unbiased estimator within the class of the estimators of the form cTm is derived, where Tm is the maximum likelihood estimate of θ. Some shrinkage testimators are proposed and their risks are computed. The relative efficiencies of the shrinkage testimators with respect to a minimum risk unbiased estimator of the form cTm under the squared log error loss function are calculated for the comparison purposes. An illustrative example is also presented.
{"title":"Shrinkage Testimation in Exponential Distribution based on Records under Asymmetric Squared Log Error Loss","authors":"M. N. Qomi, L. Barmoodeh","doi":"10.18869/ACADPUB.JSRI.12.2.225","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.2.225","url":null,"abstract":"In the present paper, we study shrinkage testimation for the unknown scale parameter θ > 0 of the exponential distribution based on record data under the asymmetric squared log error loss function. A minimum risk unbiased estimator within the class of the estimators of the form cTm is derived, where Tm is the maximum likelihood estimate of θ. Some shrinkage testimators are proposed and their risks are computed. The relative efficiencies of the shrinkage testimators with respect to a minimum risk unbiased estimator of the form cTm under the squared log error loss function are calculated for the comparison purposes. An illustrative example is also presented.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"5 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":"130837536","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.12.2.129
R. Farnoosh, A. Hajrajabi
In this paper, a skew normal state space model of RC electrical circuit is presented by considering the stochastic differential equation of the this circuit as the dynamic model with colored and white noise and considering a skew normal distribution instead of normal as the measurement noise distribution. Optimal filtering technique via sequential Monte Carlo perspective is developed for tracking the charge as the hidden state of this model. Furthermore, it is assumed that this model contains unknown parameters (resistance, capacitor, mean, variance and shape parameter of the skew normal as the measurement noise distribution). Bayesian framework is applied for estimation of both the hidden charge and the unknown parameters using particle marginal Metropolis-Hastings scheme. It is shown that the coverage percentage of skew normal is more than the one of normal as the measurement noise. Some simulation studies are carried out to demonstrate the efficiency of the proposed approaches.
{"title":"Skew Normal State Space Modeling of RC Electrical Circuit and Parameters Estimation based on Particle Markov Chain Monte Carlo","authors":"R. Farnoosh, A. Hajrajabi","doi":"10.18869/acadpub.jsri.12.2.129","DOIUrl":"https://doi.org/10.18869/acadpub.jsri.12.2.129","url":null,"abstract":"In this paper, a skew normal state space model of RC electrical circuit is presented by considering the stochastic differential equation of the this circuit as the dynamic model with colored and white noise and considering a skew normal distribution instead of normal as the measurement noise distribution. Optimal filtering technique via sequential Monte Carlo perspective is developed for tracking the charge as the hidden state of this model. Furthermore, it is assumed that this model contains unknown parameters (resistance, capacitor, mean, variance and shape parameter of the skew normal as the measurement noise distribution). Bayesian framework is applied for estimation of both the hidden charge and the unknown parameters using particle marginal Metropolis-Hastings scheme. It is shown that the coverage percentage of skew normal is more than the one of normal as the measurement noise. Some simulation studies are carried out to demonstrate the efficiency of the proposed approaches.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"286 5 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":"117342986","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 : 2015-09-15DOI: 10.18869/ACADPUB.JSRI.12.1.1
احد جمالیزاده, وحید امیرزاده, فرزانه سادات هاشمی
In this paper, we introducte a family of univariate Birnbaum- Saunders distributions arising from the skew-normal-t distribution. We ob- tain several properties of this distribution such as its moments, the maxi- mum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstrate its flexibility and conduct a simula- tion study to demonstrate the usefulness of this distribution when compared to the ordinary Birnbaum-Saunders and skew-normal Birnbaum-Saunders
{"title":"An Extension of the Birnbaum-Saunders Distribution Based on Skew-Normal-t Distribution","authors":"احد جمالیزاده, وحید امیرزاده, فرزانه سادات هاشمی","doi":"10.18869/ACADPUB.JSRI.12.1.1","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.1.1","url":null,"abstract":"In this paper, we introducte a family of univariate Birnbaum- Saunders distributions arising from the skew-normal-t distribution. We ob- tain several properties of this distribution such as its moments, the maxi- mum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstrate its flexibility and conduct a simula- tion study to demonstrate the usefulness of this distribution when compared to the ordinary Birnbaum-Saunders and skew-normal Birnbaum-Saunders","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114699027","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 : 2015-09-15DOI: 10.18869/ACADPUB.JSRI.12.1.83
S. Z. Mehryan, A. Sayyareh
Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case. In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also, based on the simulation study, we have compared the ability of some model selection criteria to select the optimal autoregressive model. Then we consider a set of real data, level of lake Huron 1875-1930, as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.
{"title":"Statistical Inference in Autoregressive Models with Non-negative Residuals","authors":"S. Z. Mehryan, A. Sayyareh","doi":"10.18869/ACADPUB.JSRI.12.1.83","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.1.83","url":null,"abstract":"Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case. In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also, based on the simulation study, we have compared the ability of some model selection criteria to select the optimal autoregressive model. Then we consider a set of real data, level of lake Huron 1875-1930, as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125431748","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 : 2015-09-15DOI: 10.18869/ACADPUB.JSRI.12.1.39
هادی امامی
Usually the existence of influential observations is complicated by the presence of collinearity in linear measurement error models. How- ever no method of influence measure available for the possible effect's that collinearity can have on the influence of an observation in such models. In this paper, a new type of ridge estimator based corrected likelihood func- tion (REC) for linear measurement error models is defined. We show when this type of ridge estimator is used to mitigate the effects of collinearity the influence of some observations can be drastically modified. We propose a case deletion formula to detect influential points in REC. As an illustrative example two real data set are analysed.
{"title":"معیارهای تأثیر در مدلهای خطای اندازهگیری خطی ریج","authors":"هادی امامی","doi":"10.18869/ACADPUB.JSRI.12.1.39","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.1.39","url":null,"abstract":"Usually the existence of influential observations is complicated by the presence of collinearity in linear measurement error models. How- ever no method of influence measure available for the possible effect's that collinearity can have on the influence of an observation in such models. In this paper, a new type of ridge estimator based corrected likelihood func- tion (REC) for linear measurement error models is defined. We show when this type of ridge estimator is used to mitigate the effects of collinearity the influence of some observations can be drastically modified. We propose a case deletion formula to detect influential points in REC. As an illustrative example two real data set are analysed.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"224 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114878627","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 : 2015-09-15DOI: 10.18869/ACADPUB.JSRI.12.1.71
L. Golshani
In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian processes.
{"title":"The Rate of Entropy for Gaussian Processes","authors":"L. Golshani","doi":"10.18869/ACADPUB.JSRI.12.1.71","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.1.71","url":null,"abstract":"In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian processes.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114711944","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 : 2015-09-15DOI: 10.18869/ACADPUB.JSRI.12.1.105
M. Razmkhah, H. Morabbi, J. Ahmadi
In this paper, a new two-sampling scheme is proposed to con- struct appropriate confidence intervals for the lower population quantiles. The confidence intervals are determined in the parametric and nonparamet- ric set up and the optimality problem is discussed in each case. Finally, the proposed procedure is illustrated via a real data set.
{"title":"Confidence Intervals for Lower Quantiles Based on Two-Sample Scheme","authors":"M. Razmkhah, H. Morabbi, J. Ahmadi","doi":"10.18869/ACADPUB.JSRI.12.1.105","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.1.105","url":null,"abstract":"In this paper, a new two-sampling scheme is proposed to con- struct appropriate confidence intervals for the lower population quantiles. The confidence intervals are determined in the parametric and nonparamet- ric set up and the optimality problem is discussed in each case. Finally, the proposed procedure is illustrated via a real data set.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133504384","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 : 2015-09-10DOI: 10.18869/ACADPUB.JSRI.12.1.57
H. A. Noughabi
Shannon entropy is increasingly used in many applications. In this article, an estimator of the entropy of a continuous random variable is proposed. Consistency and scale invariance of variance and mean squared error of the proposed estimator is proved and then comparisons are made with Vasicek’s (1976), van Es (1992), Ebrahimi et al. (1994) and Correa (1995) entropy estimators. A simulation study is performed and the results indicate that the proposed estimator has smaller mean squared error than competing estimators.
香农熵在许多应用中得到越来越多的应用。本文给出了连续随机变量熵的一个估计量。证明了所提出的熵估计量方差和均方误差的一致性和尺度不变性，并与Vasicek(1976)、van Es(1992)、Ebrahimi et al.(1994)和Correa(1995)熵估计量进行了比较。仿真研究结果表明，该估计器的均方误差小于同类估计器。
{"title":"On the Estimation of Shannon Entropy","authors":"H. A. Noughabi","doi":"10.18869/ACADPUB.JSRI.12.1.57","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.12.1.57","url":null,"abstract":"Shannon entropy is increasingly used in many applications. In this article, an estimator of the entropy of a continuous random variable is proposed. Consistency and scale invariance of variance and mean squared error of the proposed estimator is proved and then comparisons are made with Vasicek’s (1976), van Es (1992), Ebrahimi et al. (1994) and Correa (1995) entropy estimators. A simulation study is performed and the results indicate that the proposed estimator has smaller mean squared error than competing estimators.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126733890","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 : 2015-03-15DOI: 10.18869/ACADPUB.JSRI.11.2.147
H. Panahi, A. Sayyareh
Doubly censoring scheme, which includes left as well as right censored observations, is frequently observed in practical studies. In this paper we introduce a new interval say tracking interval for comparing the two rival models when the data are doubly censored. We obtain the asymptotic properties of maximum likelihood estimator under doubly censored data and drive a statistic for testing the null hypothesis that the proposed non-nested models are equally close to the true model against the alternative hypothesis that one model is closer when we are faced with an experimental situation. Monte Carlo simulations are performed to observe the behavior of the theoretical results, and the proposed methodology is illustrated with data from spreading of the micro plasma droplets. We also perform the statistical analysis of these data using the probability models including Weibull, Burr type XII, Burr type III and inverse Weibull distributions. One important result of this study is that the Burr type XII distribution, in contrast to inverse Weibull distribution, may describe more closely to Weibull distribution for spread factor data under doubly censored sample.
双审查方案，包括左和右审查的意见，在实际研究中经常被观察到。本文引入了一种新的区间，即跟踪区间，用于在数据被双重删减的情况下比较两种相互竞争的模型。我们获得了双截尾数据下最大似然估计量的渐近性质，并驱动了一个统计量，用于检验所提出的非嵌套模型与真实模型同样接近的零假设，而不是当我们面临实验情况时一个模型更接近的备用假设。通过蒙特卡罗模拟来观察理论结果的行为，并用微等离子体液滴扩散的数据来说明所提出的方法。我们还使用Weibull、Burr type XII、Burr type III和逆Weibull分布等概率模型对这些数据进行了统计分析。本研究的一个重要结果是，与逆威布尔分布相比，Burr型XII分布可以更接近威布尔分布来描述双截后样本下的传播因子数据。
{"title":"Tracking Interval for Doubly Censored Data with Application of Plasma Droplet Spread Samples","authors":"H. Panahi, A. Sayyareh","doi":"10.18869/ACADPUB.JSRI.11.2.147","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.11.2.147","url":null,"abstract":"Doubly censoring scheme, which includes left as well as right censored observations, is frequently observed in practical studies. In this paper we introduce a new interval say tracking interval for comparing the two rival models when the data are doubly censored. We obtain the asymptotic properties of maximum likelihood estimator under doubly censored data and drive a statistic for testing the null hypothesis that the proposed non-nested models are equally close to the true model against the alternative hypothesis that one model is closer when we are faced with an experimental situation. Monte Carlo simulations are performed to observe the behavior of the theoretical results, and the proposed methodology is illustrated with data from spreading of the micro plasma droplets. We also perform the statistical analysis of these data using the probability models including Weibull, Burr type XII, Burr type III and inverse Weibull distributions. One important result of this study is that the Burr type XII distribution, in contrast to inverse Weibull distribution, may describe more closely to Weibull distribution for spread factor data under doubly censored sample.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122308973","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":"توسیعی از توزیع لیندلی تعمیمیافته و کاربردهای آن برای دادههای طول عمر","authors":"حمزه ترابی, مهرانگیز فلاحتی نایینی, نرگس منتظریدهش","doi":"10.18869/ACADPUB.JSRI.11.2.203","DOIUrl":"https://doi.org/10.18869/ACADPUB.JSRI.11.2.203","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126292165","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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