One way of dealing with the problem of collinearity in linear models, is to make use of the Liu estimator. In this paper, a new estimator by generalizing the modified Liu estimator of Li and Yang (2012) has been proposed. This estimator is constructed based on a prior information of vector parameters in linear regression and the generalized estimator of Akdeniz and Kachiranlar (1995). Using the mean square error matrix criterion, we have obtained the superiority conditions Of this newly defined estimator over the generalized Liu estimator. For comparison sake, a numerical example as well as a Monte Carlo simulation study are considered.

‎This paper is investigating the mixture autoregressive model with constant mixing weights in state space form and generalization to ARMA mixture model‎. ‎Using a sequential Monte Carlo method‎, ‎the forecasting‎, ‎filtering and smoothing distributions are approximated and parameters f the model is estimated via the EM algorithm‎. ‎The results show the dimension of parameter vector in state space representation reduces‎. ‎The results of the simulation study show that the proposed filtering algorithm has a steady state close to the real values of the state vector‎. ‎Moreover‎, ‎according to simulation results‎, ‎the mean vectors of filtering and smoothing distribution converges to state vector quickly‎.

In the last decade, Poisson regression has been used for modeling count response variables. Poisson regression is not a suitable choice when count data bears superfluity of zero numbers. In this article, two models zero-inflated Poisson regression and bivariate zero-inflated Poisson regression with random effect are used to modeling count responses with a superfluity of zero numbers. Usually, distribution of the random effect is considered normal, but we intend to employ more flexible skew-normal distribution for the distribution of the random effect. Finally, the purpose model is applied to data which as obtained from the Shahid Chamran University of Ahvaz concerning the number of failed courses and fail grade point average semesters. we used a simulation method to verify parameter estimations. 

‎Usually in survey sampling when the sensitive questions are asked directly‎, ‎the respondents do not provide true answers‎. ‎The randomized response techniques have been introduced to protect the privacy responses‎. ‎In this article we focus on Simons randomized response technique for qualitative variables‎. ‎Using the combination of the two different‎ ‎Simmons’ models‎, ‎a new combined randomized response technique is introduced to increase protection of privacy‎. ‎Using simulation in R package‎, ‎efficiency of the proposed model is compared to the Simmons’ and Alavi and Tajodini's (1394) models‎. ‎Finally‎, ‎the proposed model has been employed for estimating the proportion of student cheating in Shahid Chamran University‎.

‎The parameters of reliability for the most family marginal distribution is estimated with the assumption of independence between two component stress and strength‎, ‎but‎, ‎unfortunately when these two component are correlated‎, ‎have been less discussed‎. ‎Recently‎, ‎a method based on a copula function for estimating the reliability parameter is proposed under the assumption of correlation between stress and strength components‎. ‎In this paper‎, ‎this method is used to estimate the reliability parameter when the distribution of componets is Generalized Exponential (GE)‎. ‎For this purpose FGM‎, ‎generalized FGM and frank copula function have been used‎. ‎Then simulation is also used to demonstrate the suitability of the estimates‎. ‎In the end‎, ‎reliability parameter for data relative contribution of major groups in terms of age breakdown of the population of urban and rural areas in Iran in the year 1390 will be estimated.

In many sample surveys, the variables of interest, such as student cheating in a university are sensitive in nature. In such situations, the interviewees respond to direct questions untruthful, or refuse to answer. The various indirect methods such as randomized response technique and item count technique are introduced to collect sensitive information. In this paper a new item count is proposed, then its randomized version called randomized item count model is introduced. Using this model an unbiased estimator for the sensitive proportion of the population is obtained. The variance of the estimator and an estimate for its variance are obtained. A criterion for comparing efficiency and privacy is introduced simultaneously. Using simulation, the proposed model is evaluated and its efficiency and privacy are compared with the Simons’ technique. Based on this criterion, it is shown that the proposed method is better than the Simons method. The proportion of student cheating in the Shahid Chamran University of Ahvaz is estimated using the proposed model.

‎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.

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.

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.

Redundancy and reduction are two main methods for improving system reliability. In a redundancy method, system reliability can be improved by adding extra components  to some original components of the system. In a reduction method, system reliability increases by reducing the failure rate at all or some components of the system. Using the concept of reliability equivalence factors, this paper investigates equivalence between the reduction and redundancy methods. A closed formula is obtained for computing the survival equivalence factor. This factor determines the amount of reduction in the failure rate of a system component(s) to reach the reliability of the same system when it is improved. The effect of component importance measure is also studied in our derivations.