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Showing 237 results for Type of Study: Research
Azam Rastin, Mohammadreza Faridrohani,
Volume 13, Issue 2 (2-2020)
Abstract
The methodology of sufficient dimension reduction has offered an effective means to facilitate regression analysis of high-dimensional data. When the response is censored, most existing estimators cannot be applied, or require some restrictive conditions. In this article modification of sliced inverse, regression-II have proposed for dimension reduction for non-linear censored regression data. The proposed method requires no model specification, it retains full regression information, and it provides a usually small set of composite variables upon which subsequent model formulation and prediction can be based. Finally, the performance of the method is compared based on the simulation studies and some real data set include primary biliary cirrhosis data. We also compare with the sliced inverse regression-I estimator.
Ronak Jamshidi, Sedigheh Shams,
Volume 13, Issue 2 (2-2020)
Abstract
In this paper, a family of copula functions called chi-square copula family is used for modeling the dependency structure of stationary and isotropic spatial random fields. The dependence structure of this copula is such that, it generalizes the Gaussian copula and flexible for modeling for high-dimensional random vectors and unlike Gaussian copula it allows for modeling of tail asymmetric dependence structures. Since the density function of chi-square copula in high dimension has computational complexity, therefore to estimate its parameters, a composite pairwise likelihood method is used in which only bivariate density functions are used. The purpose of this paper is to investigate the properties of the chi-square copula family, estimating its parameters with the composite pairwise likelihood and its application in spatial interpolation.
Jafar Ahmadi, Fatemeh Hooti,
Volume 13, Issue 2 (2-2020)
Abstract
In survival studies, frailty models are used to explain the unobserved heterogeneity hazards. In most cases, they are usually considered as the product of the function of the frailty random variable and baseline hazard rate. Which is useful for right censored data. In this paper, the frailty model is explained as the product of the frailty random variable and baseline reversed hazard rate, which can be used for left censored data. The general reversed hazard rate frailty model is introduced and the distributional properties of the proposed model and lifetime random variables are studied. Some dependency properties between lifetime random variable and frailty random variable are investigated. It is shown that some stochastic orderings preserved from frailty random variables to lifetime variables. Some theorems are used to obtain numerical results. The application of the proposed model is discussed in the analysis of left censored data. The results are used to model lung cancer data.
Marjan Zare, Akbar Asgharzadeh, Seyed Fazel Bagheri,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, the smallest confidence region is obtained for the location and scale parameters of the two-parameter exponential distribution. For this purpose, we use constrained optimization problems. We first provide some suitable pivotal quantities to obtain a balanced confidence region. We then obtain the smallest confidence region by minimizing the area of the confidence region using the Lagrangian method. Two numerical examples are presented to illustrate the proposed methods. Finally, some applications of proposed joint confidence regions in hypothesis testing and the construction of confidence bands are discussed.
Shadi Saeidi Jeyberi, Mohammadreza Zadkarami, Gholamali Parham,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, Bayesian fuzzy estimator is obtained first, for the fuzzy data based on the probability prior distribution and afterward based on the possible model and the possibility of a prior distribution. Considering the effect of the membership functions on the fuzzy and possibility Bayesian estimators, a membership function that gives the optimal fuzzy and possibility Bayesian estimators will be introduced for the data. The optimality of the new triangular-gaussian membership function is denoted by using the normal and exponential data sets.
Masoud Amiri, muhyiddin Izadi, baha-Eldin Khaledi,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, the worst allocation of deductibles and limits in layer policies are discussed from the viewpoint of the insurer. It is shown that if n independent and identically distributed exponential risks are covered by the layer policies and the policy limits are equal, then the worst allocation of deductibles from the viewpoint of the insurer is (d, 0, ..., 0).
Esmaeil Shirazi,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, we consider an adaptive wavelet estimation for quantile density function based on block thresholding method and obtain it's convergence rate under L2 loss function over Besove function spaces. This work is an extension of results in Chesneau et. al. (2016) and shows that the block threshold estimator gets better convergence rate (Optimal) than the estimators proposed by Chesneau et. al. (2016). The performance of the proposed estimator is investigated with a simulation study.
Elham Basiri, Seyed Mahdi Salehi,
Volume 14, Issue 1 (8-2020)
Abstract
Nowadays inference based on censored samples has been studied by many researchers. One of the most common censoring methods is progressively type II censoring. In this model, n items are put on the test. At each failure times some of the remaining items randomly withdrawn from the test. This process continues until for a pre-fixed value as m, failure times of m items are observed. For determining the best number for the items on the test different criteria can be considered. One of the most important factors that can be considered is the cost criterion. In this paper, by considering cost function and Weibull distribution for the lifetime of items, we find the optimal value for the sample size, i.e. n. In order to evaluate, the obtained results one example based on real data is given.
Mehrnaz Mohammadpour, Masoumeh Shirozhan,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, we introduce a new integer-valued autoregressive model of first order based on the negative binomial thinning operator, where the noises are serially dependent. Some statistical properties of the model are discussed. The model parameters are estimated by maximum likelihood and Yule-Walker methods. By a simulation study, the performances of the two estimation methods are studied. This survey was carried out to study the efficiency of the new model by applying it on real data.
Mohadaseh Khayyat, Rasool Rozegar, Ghobad Barmalzan,
Volume 14, Issue 1 (8-2020)
Abstract
The modified proportional hazard rates model, as one of the flexible families of distributions in reliability and survival analysis, and stochastic comparisons of (n-k+1) -out-of- n systems comprising this model have been introduced by Balakrishnan et al. (2018). In this paper, we consider the modified proportional hazard rates model with a discrete baseline case and investigate ageing properties and preservation of the usual stochastic order, hazard rate order and likelihood ratio order in this family of distributions.
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.
Shahram Yaghoobzadeh,
Volume 14, Issue 1 (8-2020)
Abstract
In this study, the E-Bayesian estimation of the reliability parameter, R = P(Y < X < Z), when X, Y and Z are three independent inverse Rayleigh distribution with different parameters, were estimated based on ranked set sampling method. To assess the efficiency of the obtained estimates, we compute the average absolute bias and relative efficiency of the derived estimates and compare them with those based on the corresponding simple random sample through Monte Carlo simulations. Also, E-Bayesian estimation of R is compared with its maximum likelihood estimation in each method. Finally, three real data sets are used to analyze the estimation methods.
Ebrahim Amini Seresht, Ghobad Barmalzan,
Volume 14, Issue 2 (2-2021)
Abstract
This paper examines the problem of stochastic comparisons of k-out-of-n systems with independent multiple-outlier scale components. In this regard, we first consider a k-out-of-n system comprising multiple-outlier scale components and then, by using a permanent function, investigate the likelihood ratio order between these systems.
Elham Basiri,
Volume 14, Issue 2 (2-2021)
Abstract
When a system is used, it is often of interest to determine with what probability it will work longer than a pre-fixed time. In other words, determining the reliability of this system is of interest. On the other hand, the reliability of each system depends on the structure and reliability of its components. Therefore, in order to improve the reliability of the system, the reliability of its components should be improved. For this purpose, it is necessary to carry out maintenance operations, which will increase costs. Another way to increase the reliability of systems is to change the location of the components. In this paper, the location of system components and optimal maintenance period are determined by minimizing the costs and maximizing the reliability of a series-parallel system. Finally, a numerical example is presented to evaluate the results in the paper.
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.
Seyede Toktam Hosseini, Jafar Ahmadi,
Volume 14, Issue 2 (2-2021)
Abstract
In this paper, using the idea of inaccuracy measure in the information theory, the residual and past inaccuracy measures in the bivariate case are defined based on copula functions. Under the assumption of radial symmetry, the equality of these two criteria is shown, also by the equality between these two criteria, radially symmetrical models are characterized. A useful bound is provided by establishing proportional (inverse) hazard rate models for marginal distributions. Also, the proportional hazard rate model in bivariate mode is characterized by assuming proportionality between the introduced inaccuracy and its corresponding entropy. In addition, orthant orders are used to obtain inequalities. To illustrate the results, some examples and simulations are presented.
Akram Kohansal, Nafiseh Alemohammad, Fatemeh Azizzadeh,
Volume 14, Issue 2 (2-2021)
Abstract
The Bayesian estimation of the stress-strength parameter in Lomax distribution under the progressive hybrid censored sample is considered in three cases. First, assuming the stress and strength are two random variables with a common scale and different shape parameters. The Bayesian estimations of these parameters are approximated by Lindley method and the Gibbs algorithm. Second, assuming the scale parameter is known, the exact Bayes estimation of the stress-strength parameter is obtained. Third, assuming all parameters are unknown, the Bayesian estimation of the stress-strength parameter is derived via the Gibbs algorithm. Also, the maximum likelihood estimations are calculated, and the usefulness of the Bayesian estimations is confirmed, in comparison with them. Finally, the different methods are evaluated utilizing the Monte Carlo simulation and one real data set is analyzed.
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.
Reza Zarei, ,
Volume 14, Issue 2 (2-2021)
Abstract
In this paper, the Bayesian and empirical Bayesian approaches studied in estimate the multicomponent stress–strength reliability model when the strength and stress variables have a generalized Rayleigh distribution with different shape parameters and identical scale parameter. The Bayesian, empirical Bayesian and maximum likelihood estimation of reliability function is obtained in the two cases known and unknown of scale parameter under the mean squared error loss function. Then, these estimators are compared empirically using Monte Carlo simulation and two real data sets.
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