JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY)
Year:2013 | Volume:13 | Issue:3|Papers Count:7

Copula functions are powerful tools for construction the multivariate distribution of dependent variables in terms of their marginal distributions. Each of these functions provide a model which represents all properties of the variables dependency. For spatial data analysis, the dependence structure of the data should be determined by using the multivariate distribution of the random field. In analysis of Spatio-temporal data it is also necessary to identify the relations between spatial and temporal structure of the data in terms of Spatio-temporal covariance function. Sometimes a separable Spatio-temporal covariance function is used for the ease of application, but in some applications this property is not realistic. In these cases it is required to use a non-separable Spatio-temporal covariance function. In this paper the role of copula functions in determination of joint distribution of a random field is considered and the properties of a valid spatial copula function are determined. Then a new valid spatial copula family is introduced. Next some spatial and nonseparable Spatio-temporal covariance functions are constructed by using these copula functions.

In this study, we simulate numerically the process of oxygen mass transport in the human circulatory system incorporating the contribution of axial diffusion. Simulated equation is a time dependent convective-diffusion partial differential equation wherein has applicable application in the bioengineering problems such as boundary layer of fluids, electrical circuits in cables and mass transport problems.The analytical solution of this kind of equations is complicated. Therefore, the numerical solution for obtaining the approximate solution is important and the convergence and stability in this method of solution, is always a question. In this study, we try to answer the above questions with respect to this special equation and for this we use finite differences.

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models, such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models, since there are the latent variables and non-Gaussian spatial response variables, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions, that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method, the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally, the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.

In this papear, we produce the method for formation and recognizing boundary layers in singular perturbation problems. This method involves four step for localization of non-local boundary conditions to local case. For the given problem some sufficient and necessary conditions are given for formation and non formation of boundary layers. Since the existence of boundary layers and their places has a direct relation with the structure of approximate solutions and uniform solutions, therefore the main purpose of this paper is recognition and formation of boundary layers in singular perturbation problems with non-local boundary conditions. This process will be done by using fundamental solution of adjoint given differential equation and necessary conditions. In fact by using these necessary conditions and given boundary conditions, we make an algebraic system. By solving this algebraic system by Cramer rule we obtain boundary values of unknown function. These values of unknown function are local boundary conditions. The mathematical model for this kind of problem usually is in the form of either ordinary differential equations (O.D.E) or partial differential equations (P.D.E) in which the highest derivative is multiplied by some powers of as a positive small parameter.

Monitoring process mean and variance simultaneously in a single control chart simplifies the process monitoring. If in addition, a simultaneous control chart is capable of recognizing the source of contamination, this capability leads to additional simplicity. These are the reasons why simultaneous control charts have attracted many researchers and manufacturers. Recently, in the statistical process control literature some control charts have been introduced which are based on the idea of Bayesian predictive density. This type of control charts, not only brings into account the uncertainty concerning the estimation of unknown parameters, but also do not need extensive simulations for computation of control limits. These control charts have been introduced for mean and variance in both univariate and multivariate situations. Up to now, no simultaneous control chart has been introduced based on Bayesian predictive density. In this paper, using the idea of Bayesian predictive density, we introduce a new simultaneous control chart for monitoring univariate mean and variance. We illustrate the important capabilities of this new chart through simulated data. This new chart is applicable when parameters are unknown. In other words, it brings into account the uncertainty concerning the unknown parameters. This chart is able to recognize the source of contamination and is sensitive to small changes in the mean and variance. In this chart the control limits, needless of simulation, can simply be obtained from normal table.

There are several methods for goodness of fit test for the skew normal distribution. This work focused on method of Meintanis [8] which is based on the empirical moment generating function. This test is discussed for the known and the unknown shape parameter. Meintanis [8] claimed that power of his test is higher than the Kolmogorov-Smirnov test. But this claim is true only for the known shape parameter. In this paper, we provide a new method for finding his test statistic that has more efficiency. Also Meintanis [8] not determine the size of himself test for the known shape parameter which in this paper we will determine it.

In the Bayesian framework, robust Bayesian methods concern on estimation of unknown parameters, or prediction of future observation, by specifying a class of priors instead of a single prior. Robust Bayesian methods have been used extensively in actuarial sciences for estimation of premium and prediction of future claim size. In this paper we consider robust Bayes estimation of premium and prediction of future claim size under two classes of prior distribution and under the scale invariant squared error loss function. Finally, by a simulation study and using prequential analysis, we compare the obtained robust Bayes estimators of future claim size.