مجله علوم آماری
سال سیزدهم شماره 2 (پیاپی 26، پاییز و زمستان 1398)

‎This paper will analyze inflated bivariate mixed count data‎. ‎The estimations of model parameters are obtained by the maximum likelihood method‎. ‎For a bivariate case which has inflation in one or two points‎, ‎the new bivariate inflated power series distributions are presented‎. ‎These inflated distributions are used in joint modeling of bivariate count responses‎. ‎Also‎, ‎to illustrate the utility of the proposed models‎, ‎some simulation studies are performed‎. ‎and finally‎, ‎a real dataset is analyzed‎.

‎We introduce a modified Poisson sampling‎, ‎with a fixed lower bound of sample size‎. ‎The design is‎ ‎a combination of simple random sampling and Poisson sampling‎. ‎Simple random sampling is used to‎ ‎compensate for the lack of sample size from remaining elements in the finite population‎, ‎after execution of a‎ ‎Poisson sampling‎. ‎At the first stage‎, ‎the units are sampled independently with given inclusion probabilities‎. ‎But in the‎ ‎second stage‎, ‎inclusion probabilities are dependent to each other‎. ‎Because it is important to know‎, ‎which‎ ‎of the elements are selected in the first stage and which of them are remained‎. ‎Some advantages of our‎ ‎design are‎: ‎simple performance‎, ‎controlling sample size‎, ‎ability to perform the method of probability‎ ‎proportional to size‎. ‎The simulations show that the design can‎ ‎dominate its rival design in probability proportional to size sampling‎.

‎This paper examines the problem of stochastic‎ ‎comparisons of series and parallel systems with independent and heterogeneous components generalized linear failure rate‎. ‎First‎, ‎we consider two series system with possibly different parameters and obtain the usual stochastic order between the series systems‎. ‎Next‎, ‎we drive the usual stochastic order between parallel systems‎. ‎We also discuss the usual stochastic order between parallel systems by using the unordered majorization and the weighted majorization order between the parameters on the Ɗп.

In this paper, the Bootstrap and Jackknife methods are stated and using these methods, entropy is estimated. Then the estimators based on Bootstrap and Jackknife are investigated in terms of bias and RMSE using simulation. The proposed estimators are compared with other entropy estimators by Monte Carlo simulation. Results show that the entropy estimators based on Bootstrap and Jackknife have a good performance as compared to the other estimators. Next, some tests of normality based on the proposed estimators are introduced and the power of these tests are compared with other tests.

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.

‎The performance of a system depends not only on its design and operation but also on the servicing and maintenance of the item during its operational lifetime‎. ‎Thus‎, ‎the repair and maintenance are important issues in the reliability‎. ‎In this paper‎, ‎a repairable k-out-of-n system is considered that starts operating at time 0‎. ‎If the system fails‎, ‎then it undergoes minimal repair and begins to operate again‎. ‎The reliability function‎, ‎hazard rate function‎, ‎mean residual life function and some reliability properties of the system are obtained by using the connection between the concepts of minimal repair and record values‎. ‎Some known stochastic orders are also used to compare the lifetimes and residual lifetimes of two repairable k-out-of-n systems‎. ‎Finally‎, ‎based on the given information about the lifetimes of k-out-of-n systems‎, ‎some prediction intervals for the lifetime of the proposed repairable system are obtained‎.

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.

‎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 many fields such as econometrics‎, ‎psychology‎, ‎social sciences‎, ‎medical sciences‎, ‎engineering‎, ‎etc.‎, ‎we face with multicollinearity among the explanatory variables and the existence of outliers in data‎. ‎In such situations‎, ‎the ordinary least-squares estimator leads to an inaccurate estimate‎. ‎The robust methods are used to handle the outliers‎. ‎Also‎, ‎to overcome multicollinearity ridge estimators are suggested‎. ‎On the other hand‎, ‎when the error terms are heteroscedastic or correlated‎, ‎the generalized least squares method is used‎. ‎In this paper‎, ‎a fast algorithm for computation of the feasible generalized least trimmed squares ridge estimator in a semiparametric regression model is proposed and then‎, ‎the performance of the proposed estimators is examined through a Monte Carlo simulation study and a real data set.

The non-homogeneous bivariate compound Poisson process with short term periodic intensity function is used for modeling the events with seasonal patterns or periodic trends. In this paper, this process is carefully introduced. In order to characterize the dependence structure between jumps, the Levy copula function is provided. For estimating the parameters of the model, the inference for margins method is used. As an application, this model is fitted to an automobile insurance dataset with inference for margins method and its accuracy is compared with the full maximum likelihood method. By using the goodness of fit test, it is confirmed that this model is appropriate for describing the data.

In this study, the E-Bayesian and hierarchical Bayesian for stress-strength, when X and Y are two independent Rayleigh distributions with different parameters were estimated based on the LINEX loss function. These methods were compared with each other and with the Bayesian estimator using Monte Carlo simulation and two real data sets.

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 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 this paper, we study a three-parameter bivariate distribution obtained by taking Geometric minimum of Rayleigh distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.