In this paper we propose a new distribution based on Weibull distribution. This distribution has three parameters which displays increasing, decreasing, bathtub shaped, unimodal and increasing-decreasing-increasing failure rates. Then consider characteristics of this distribution and a real data set is used to compared proposed distribution whit some of the generalized Weibull distribution.

In weighted sampling as a generalization of random sampling, every observation, y, is recorded with probably proportional to a non-negative function of y. In this paper, the normal regression model is investigated under the weighted sampling for a common weight function. Parameters of the model are estimated for known and unknown weight parameters. Using simulation, efficiency of estimators is studied when they have not closed forms. As an application, the data of number of visited  patients by specialist doctors in Social Security Organization of Ahvaz in Iran (SSOAI) are analyzed.

The standard Beta distribution is a suitable distribution for modeling the data that include proportions. In many situations which the data of proportions include a considerable number of zeros and ones, the inflated beta distributions are more appropriate. When probabilities of recording such observations are proportional to a nonnegative weight function, the recorded observations distributed as a weighted inflated Beta. This article focuses on the size biased inflated Beta distribution as a special case of weighted inflated Beta distribution with the power weight function. Some properties of this distribution is studied and its parameters are estimated using maximum likelihood and method of moments approaches. The estimators are compared via a simulation study. Finally, the real mortality data set is fitted for this model.

In this paper a method has been given to detect the shocks in structural time series using Kalman filter algorithm. As the Kalman filter algorithm is used for state space forms which include ARMA models as an especial case, the suggested method can be used for more general time series than linear models. Five shocks; additive outlier, level change, seasonal change, periodic change and slope change have been reviewed with this method. The performance of suggested method has been shown via a simulation study. The marriage data set from England has been considered as a real data set to study.

In this paper, using Band matrix, a method has been proposed to estimating the covariance matrix of the ARMA model and the likelihood function of the ARMA model with diagonal covariance matrix has been obtained and approximations for Kullback-Leibler and Chernoff criteria were presented. In addition, two rules for discriminating the ARMA models has been proposed. A simulation and real data sets are used to illustrate the performance of the proposed rules. Significant reduction of the calculations for large time series and low discrimination error rate are two characteristics of the proposed rules. In addition no need to normal assumption is showed in a theorem.

‎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.

Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated variances and so an inappropriate inference. In this paper, the Gaussian spatial model is fitted based on covariate measurement error. For this purpose, we adopt the Bayesian approach and utilize the Markov chain Monte Carlo algorithms and data augmentations to carry out calculations. The methodology is illustrated using simulated data.

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. 

The study of regression diagnostic, including identification of the influential observations and outliers, is of particular importance. The sensitivity of least squares estimators to the outliers and influential observations lead to extending the regression diagnostic in order to provide criteria to assess the anomalous observations. Detecting influential observations and outliers in the presence of collinearity is a complicated task, in the sense that collinearity may cover some of the unusual data. One of the considerable methods to identify outliers is the mean shift outliers method. In this article, we extend the mean shift outliers method to the ridge estimates under linear stochastic restrictions, which is used to reduce the effect of collinearity, and to provide the test statistic to identify the outliers in these estimators. Finally, we show the ability of our proposed method using a practical example of real data.

‎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.