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In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed distributions, such as the skew-t and the skew slash, as special cases and is recommended as an alternative to the normal distribution. The statistical inference based on the maximization of marginal likelihoods is complicated, in general, for non-linear regression models and thus we implement the MCMC approach to obtain Bayes estimates. Finally, we fit a non-linear regression model using proposed distributions for a real data set to show the importance of the recommended model.

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‎A popular application of nonlinear models with mixed effects pharmacokinetic studies‎, ‎in which the distribution of used drug during the life of the individual study‎. ‎The fit of these models assume normality of the random effects and errors are common‎, ‎but can not make it invalid results in the estimation‎. ‎In longitudinal data analysis‎, ‎typically assume that the random effects and random errors are normally distributed‎, ‎but there is a possible violation of empirical studies‎. ‎For this reason‎, ‎the analysis of the pharmacokinetic data such as normal distribution‎, ‎slashe‎, ‎t‎ - ‎student and Contaminated normal considered to be based on analytical achieved‎. ‎In this paper‎, ‎parameter estimation of nonlinear models with mixed effects on the maximum likelihood estimation method and the Bayesian approach respectively by SAS software and Open Bugs pharmacokinetic data set for being carried out‎. ‎Also‎, ‎using the model selection criteria are based on these two approaches‎, ‎we found the best fit model to the data‎.

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‎The goal of this paper is to introduce the contraction method for analysing the algorithms‎.

‎By means of this method several interesting classes of recursions can be analyzed as paricular cases of the general framework‎. ‎The main steps of this technique is based on contraction properties of algorithm with respect to suitable probability metrics‎. ‎Typlically the limiting distribution is characterized as a fixed poin of a limiting operator on the class of probability distributions‎.‎

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In conventional methods for spatial survival data modeling, it is often assumed that the coefficients of explanatory variables in different regions have a constant effect on survival time. Usually, the spatial correlation of data through a random effect is also included in the model. But in many practical issues, the factors affecting survival time do not have the same effects in different regions. In this paper, we consider the spatial effects of factors affecting survival time are not the same in the different areas.
For this purpose, spatial regression models and spatial varying coefficient models are introduced. Next, the Bayesian estimates of their parameters are presented. Three models of classical regression, spatial regression and spatial varying coefficient regression are used to analyze Esophageal cancer survival data. The relative risk of various factors is examined and evaluated.

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The main ‎goal‎ of this paper is to investigate the site and bond percolation of the lattice $mathbb{Z}^2‎$‎. The main symbols and concepts, including critical probabilities, are introduced. Bethe lattice and $k$-branching trees are examined and finally lattice

$mathbb{Z}^2‎$ is considered. The fundamental theorem of Harris and Kesten that presents the lower and upper bounds of the critical probability on the lattice $mathbb{Z}^2‎$ expresses and proves.

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Knowledge of statistics, ever since its inception, has served every aspect of human life and every individual and social class. It has shown its extraordinary potential in dealing with numerous problems encountering human beings since the occurring of Covid-19 in Wuhan, China. A vast amount of literature has appeared showing the power of the science of statistics in answering different questions regarding this disease and all its consequences. But it comes short of, as an instance, in modelling the geometry of disease spread among societies and in the world as a whole. Here the only way to deal with this matter is to resort to probability theory and its many ramifications in providing realistic models in describing this spread. A very power tool in this regard is percolation theory, which besides its many applications in mathematical physics, is very handy in modelling epidemic diseases, among them the Covid-19.  A short description of this theory with its use in modelling the spread of epidemic deceases, shows the importance of dealing with probability as a separate subject in the curricula and not a subordinate of the science of statistics which is now dominant in the statistics major curricula in the Iranian schools.