فصلنامه مدل سازی پیشرفته ریاضی
سال هشتم شماره 2 (پاییز و زمستان 1397)

Spatial statistics is the analytical science of spatial correlated data. In environmental fields of studies that deal with spatially correlated data due to their location in a given area, on the other hand, in the survey sampling it is assumed that the sample is taken from a population with independent units. This assumption is used at all stages of sampling, analysis and modeling. But when the units of the study population are correlated, the entire process, such as sampling methods and statistical process requires review and the entire process will be considering the correlation structure. In the classic sampling methods from a variable, when some covariates exist, then the balanced sampling is used for improving the quality of sample. In this paper, we introduce spatial balanced sampling design where the components of the spatial locations are considered as covariates. Then in an intensive simulation study Is shown that the kriging error induced by our sampling method is less than foe the other available methods. Finally, the application of the proposed method is shown in a real example.

Normal residual is one of the usual assumptions in autoregressive model but sometimes in practice we are faced with non-negative residuals. In this paper, we have considered the autoregressive time series model where the residuals follow exponential and Weibull family. The estimation of the parameters in autoregressive with non-negative residuals are studied based on the modified maximum likelihood, bootstrap and moments estimators. We examine by simulation, the performance of the proposed estimation methods and found that the bootstrap estimator is the better one for autoregressive model with non-negative residuals. As a real data analysis, we have considered the S&P500 data between 1987-2015 as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.

In this paper, we study LARCH processes with periodic structure as a new class of time series with periodic conditional heteroscedasticity and long memory property. We characterize the structure of inter and intra season correlations.
Under the proposed assumptions, the long memory property for each season is studied too. Finally, by simulation study the efficiency of the R/S estimator for estimating long memory parameter of each season is shown.

In this article, estimation of a dynamic reliability measure based on ranked set sampling is studied when stress and strength variables are dependent. The proposed estimator is compared with the analogous estimator in simple random sampling theoretically and numerically. The results show that estimation using ranked set sampling design is often more precise. Also, the difference in precision of the two estimators is more pronounced as the correlation coefficient between stress and strength variables goes higher.

This paper is concerned with the numerical solutions of a mathematical model of coupled plankton–oxygen dynamics. About 70% of the atmospheric oxygen is produced by the photosynthetic activity of phytoplankton and the phytoplankton activities are affected by the ocean dynamics. So, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. A mode describing plankton–oxygen dynamics is considered. For discretizing the model which is a system of nonlinear differential equations, a combination of finite differences and meshless methods are used. The time variable is discretized by forward finite difference scheme. Because of the high accuracy of meshless methods, in the space dependent model, a meshless approach is proposed for discretizing the space variable. The method uses the strong form equation and collocation approach for discretization. Multiquadrics radial basis functions are used which have the approximation power of exponential order. Numerical results reveal that in a specific domain of oxygen production the model is stable. Also, it is shown that global warming will affect the system, resulting in the oxygen reduction and plankton extinction.

Let A be a row-finite k-graph and K a field. In this paper, we investigate decomposability of the Kumjian-Pask algebra KP(A) and the C* –algebra C*(A) associated to A. In particular, we give equivalent condition on A and its groupoid G_A for the decomposability. Moreover, we propose certain conditions under that KP(A) is a direct sum of indecomposable Kumjian-Pask algebras.