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:: Search published articles ::

Mahdi Teimouri,
Volume 14, Issue 1 (8-2020)
Abstract

‎The class of α-stable distributions incorporates both heavy tails and skewness and so are the most widely used class of distributions in several fields of study which incorporates both the skewness and heavy tails‎. ‎Unfortunately‎, ‎there is no closed-form expression for the density function of almost all of the members of this class‎, ‎and so finding the maximum likelihood estimator for the parameters of this distribution is a challenging problem‎. ‎In this paper‎, ‎in order to tackle this issue‎, ‎we propose some type of EM algorithm‎. ‎The performance of the proposed EM algorithm is demonstrated via simulation and analyzing three sets of real data‎.

Mahmood Afshari, Abouzar Bazyari, Yeganeh Moradian, Hamid Karamikabir,
Volume 14, Issue 2 (2-2021)
Abstract

In this paper, the wavelet estimators of the nonparametric regression function based on the various thresholds under the mixture prior distribution and the mean square error loss function in Bosove space are computed. Also, using a simulation study the optimality of different wavelet thresholding estimators such as posterior mean, posterior median, Bayes factor, universal threshold and sure threshold are investigated. The results show that the average mean square error of sure threshold estimator is less than the other obtained estimators. 

Mehran Naghizadeh Qomi,
Volume 14, Issue 2 (2-2021)
Abstract

In classical statistics, the parameter of interest is estimated based on sample information and using natural estimators such as maximum likelihood estimators. In Bayesian statistics, the Bayesian estimators are constructed based on prior knowledge and combining with it sample information. But, in some situations, the researcher has information about the unknown parameter as a guess. Bayesian shrinkage estimators can be constructed by Combining this non-sample information with sample information together with the prior knowledge, which is in the area of semi-classical statistics. In this paper, we introduce a class of Bayesian shrinkage estimators for the Weibull scale parameter as a generalization of the estimator at hand and consider the bias and risk of them under LINEX loss function. Then, the proposed estimators are compared using a real data set. 

Mousa Abdi, Mohsen Madadi, Ahad Jamalizadeh,
Volume 14, Issue 2 (2-2021)
Abstract

In this article, a mixture of multivariate normal and standard exponential distributions is investigated. It is shown that the range of skewness and kurtosis coefficients for this distribution is wider than that of the skew-normal distribution. Some properties of this distribution, such as characteristic function, moment generating function, four first moments, skewness and kurtosis of distribution are presented. Also, the distribution of offine transformations and canonical forms of distribution are derived. The maximum likelihood estimation of parameters of the model is computed by using an EM algorithm. To investigate the suitability and efficiency of the model, a simulation study is presented. Finally, two numerical examples with real data sets are studied.

Mohammad Reaz Kazemi,
Volume 14, Issue 2 (2-2021)
Abstract

In this paper, we investigate the confidence interval for the parameter of the common correlation coefficient of several bivariate normal populations. To do this, we use the confidence distribution approach. By simulation studies and using the concepts of coverage probability and expected length, We compare this method with the generalized variable approach. Results of simulation studies show that the coverage probability of the proposed method is close to the nominal level in all situations and also, in most cases, the expected length of this method is less than that of the generalized variable approach. Finally, we present two real examples to apply this approach.

Mozhgan Taavoni, Mohammad Arashi,
Volume 14, Issue 2 (2-2021)
Abstract

This paper considers the problem of simultaneous variable selection and estimation in a semiparametric mixed-effects model for longitudinal data with normal errors. We approximate the nonparametric function by regression spline and simultaneously estimate and select the variables under the optimization of the penalized objective function. Under some regularity conditions, the asymptotic behaviour of the resulting estimators is established in a high-dimensional framework where the number of parametric covariates increases as the sample size increases. For practical implementation, we use an EM algorithm to selects the significant variables and estimates the nonzero coefficient functions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed to illustrate the proposed procedure. 

Bahram Tarami, Mohsen Avaji, Nahid Sanjari Farsipour,
Volume 15, Issue 1 (9-2021)
Abstract

In this paper, using the extended Weibull Marshall-Olkin-Nadarajah family of distributions, the exponential, modified Weibull, and Gompertz distributions are obtained, and density, survival, and hazard functions are simulated. Next, an algorithm is presented for the simulation of these distributions. For exponential case, Bayesian statistics under squared error, entropy Linex, squared error loss functions and modified Linex are calculated. Finally, the presented distributions are fitted to a real data set.

Zahra Khadem Bashiri, Ali Shadrokh, Masoud Yarmohammadi,
Volume 15, Issue 1 (9-2021)
Abstract

One of the most critical discussions in regression models is the selection of the optimal model, by identifying critical explanatory variables and negligible variables and more easily express the relationship between the response variable and explanatory variables. Given the limitations of selecting variables in classical methods, such as stepwise selection, it is possible to use penalized regression methods. One of the penalized regression models is the Lasso regression model, in which it is assumed that errors follow a normal distribution. In this paper, we introduce the Bayesian Lasso regression model with an asymmetric distribution error and the high dimensional setting. Then, using the simulation studies and real data analysis, the performance of the proposed model's performance is discussed.


Morteza Mohammadi, Mahdi Emadi, Mohammad Amini,
Volume 15, Issue 1 (9-2021)
Abstract

Divergence measures can be considered as criteria for analyzing the dependency and can be rewritten based on the copula density function. In this paper, Jeffrey and Hellinger dependency criteria are estimated using the improved probit transformation method, and their asymptotic consistency is proved. In addition, a simulation study is performed to measure the accuracy of the estimators. The simulation results show that for low sample size or weak dependence, the Hellinger dependency criterion performs better than Kullback-Libeler and Jeffrey dependency criteria. Finally, the application of the studied methods in hydrology is presented.

Ehsan Golzade Gervi, Parviz Nasiri, Mahdi Salehi,
Volume 15, Issue 1 (9-2021)
Abstract

The empirical Bayes estimation of the exponential distribution parameter under squared error and LINEX loss functions is investigated when the record collects the data ranked set sampling scheme method. Then, point and interval predictions for future record values are studied. The results of this sampling scheme are compared with the products of the inverse sampling scheme. To compare the accuracy of estimators, Bayes risk and posterior risk criteria are used. These point predictors are compared in the sense of their mean squared prediction errors. To evaluate the prediction intervals for both the sampling schemes, the average interval length and coverage probability are computed and compared. In the present study, the hyperparameters are estimated in two methods. By studying the simulation and presenting real data, the estimation methods are compared, and the performance of the introduced schemes is evaluated.

Ahad Malekzadeh, Asghar Esmaeli-Ayan, Seyed Mahdi Mahmodi,
Volume 15, Issue 1 (9-2021)
Abstract

The panel data model is used in many areas, such as economics, social sciences, medicine, and epidemiology. In recent decades, inference on regression coefficients has been developed in panel data models. In this paper, methods are introduced to test the equality models of the panel model among the groups in the data set. First, we present a random quantity that we estimate its distribution by two methods of approximation and parametric bootstrap. We also introduce a pivotal quantity for performing this hypothesis test. In a simulation study, we compare our proposed approaches with an available method based on the type I error and test power. We also apply our method to gasoline panel data as a real data set.


Mohammad Hossein Poursaeed,
Volume 15, Issue 1 (9-2021)
Abstract

In this paper, based on an appropriate pivotal quantity, two methods are introduced to determine confidence region for the mean and standard deviation in a two parameter uniform distribution, in which the application of numerical methods is not mandatory. In the first method, the smallest region is obtained by minimizing the confidence region's area, and in the second method, a simultaneous Bonferroni confidence interval is introduced by using the smallest confidence intervals. By the comparison of area and coverage probability of the introduced methods, as well as, comparison of the width of strip including the standard deviation in both methods, it has been shown that the first method has a better efficiency. Finally, an approximation for the quantile of F
distribution used in calculating the confidence regions in a special case is presented.

Firozeh Bastan, Seyed Mohamad Taghi Kamel Mirmostafaee,
Volume 15, Issue 2 (3-2022)
Abstract

In this paper, estimation and prediction for the Poisson-exponential distribution are studied based on lower records and inter-record times. The estimation is performed with the help of maximum likelihood and Bayesian methods based on two symmetric and asymmetric loss functions. As it seems that the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings within Gibbs and importance sampling methods are applied to approximating these integrals. Moreover, the Bayesian prediction of future records is also investigated. A simulation study and an application example are presented to evaluate and show the applicability of the paper's results and also to compare the numerical results when the inference is based on records and inter-record times with those when the inference is based on records alone. 


Mehdi Balui, Einolah Deiri, Farshin Hormozinejad, Ezzatallah Baloui Jamkhaneh,
Volume 15, Issue 2 (3-2022)
Abstract

In most practical cases, to increase parameter estimation accuracy, we need an estimator with the least risk. In this, contraction estimators play a critical role. Our main purpose is to evaluate the efficiency of some shrinkage estimators of the shape parameter of the Pareto-Rayleigh distribution under two classes of shrinkage estimators. In this research, the purpose estimators' efficiency will be compared with the unbiased estimator obtained under the quadratic loss function. The relationship between these two classes of shrinkage estimators was examined, and then the relative efficiency of the proposed estimators was discussed and concluded via doing a Monte Carlo simulation.

Anis Iranmanesh, Farzaneh Oliazadeh, Vahid Fakoor,
Volume 15, Issue 2 (3-2022)
Abstract

In this article, we propose two non-parametric estimators for the past entropy based on length-biased data, and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length-biased random variables.

Sakineh Dehghan, Mohamadreza Faridrohani,
Volume 15, Issue 2 (3-2022)
Abstract

The concept of data depth has provided a helpful tool for nonparametric multivariate statistical inference by taking into account the geometry of the multivariate data and ordering them. Indeed, depth functions provide a natural centre-outward order of multivariate points relative to a multivariate distribution or a given sample. Since the outlingness of issues is inevitably related to data ranks, the centre-outward ordering could provide an algorithm for outlier detection. In this paper, based on the data depth concept, an affine invariant method is defined to identify outlier observations. The affine invariance property ensures that the identification of outlier points does not depend on the underlying coordinate system and measurement scales. This method is easier to implement than most other multivariate methods. Based on the simulation studies, the performance of the proposed method based on different depth functions has been studied. Finally, the described method is applied to the residential houses' financial values of some cities of Iran in 1397.

Parviz Nasiri, Raouf Obeidi,
Volume 16, Issue 1 (9-2022)
Abstract

This paper presents the inverse Weibull-Poisson distribution to fit censored lifetime data. The parameters of scale, shape and failure rate are considered in terms of estimation and hypothesis testing, so the parameters are estimated under the type-II of censorship using the maximum likelihood and Bayesian methods. In Bayesian analysis, the parameters are estimated under different loss functions. The simulation section presents the symmetric confidence interval and HPD, and the estimators are compared using statistical criteria. Finally, the model's goodness of fit is evaluated using an actual data set.

Alla Alhamidah, Mehran Naghizadeh, ,
Volume 16, Issue 2 (3-2023)
Abstract

This paper discusses the  Bayesian and E-Bayesian estimators in Burr type-XII model is discussed. The estimators are obtained based on type II censored data under the bounded reflected gamma loss function. The relationship between E-Bayesian estimators and their asymptotic properties is presented. The performance of the proposed estimators is evaluated using Monte Carlo simulation.
Mr Arta Roohi, Ms Fatemeh Jahadi, Dr Mahdi Roozbeh, Dr Saeed Zalzadeh,
Volume 17, Issue 1 (9-2023)
Abstract

‎The high-dimensional data analysis using classical regression approaches is not applicable, and the consequences may need to be more accurate.
This study tried to analyze such data by introducing new and powerful approaches such as support vector regression, functional regression, LASSO and ridge regression. On this subject, by investigating two high-dimensional data sets  (riboflavin and simulated data sets) using the suggested approaches, it is progressed to derive the most efficient model based on three criteria (correlation squared, mean squared error and mean absolute error percentage deviation) according to the type of data.


Shahrastani Shahram Yaghoobzadeh,
Volume 17, Issue 1 (9-2023)
Abstract

In this article, it is assumed that the arrival rate of customers to the queuing system M/M/c has an exponential distribution with parameter $lambda$ and the service rate of customers has an exponential distribution with parameter $mu$ and is independent of the arrive rate. It is also assumed that the system is active until time T. Under this stopping time, maximum likelihood estimation and bayesian estimation under general entropy loss functions and weighted error square, as well as under-informed and uninformed prior distributions, the system traffic intensity parameter M/M/c and system stationarity probability are obtained. Then the obtained estimators are compared by Monte Carlo simulation and a numerical example to determine the most suitable estimator.

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مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

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