Abstract: Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we used Gaussian mixture model to the pixels of an image. The parameters of the model were estimated by EM-algorithm.   In addition pixel labeling corresponded to each pixel of true image was made by Bayes rule. In fact,...

Mixed models are widely used to analyze longitudinal data. In their conventional formulation as linear mixed models (LMMs) and generalized LMMs (GLMMs), a commonly indispensable assumption in settings involving longitudinal non-Gaussian data is that the longitudinal observations from subjects are conditionally independent, given subject-specific random effects. Although conventional Gaussian...

The main aim of this work is to introduce the Gaussian Pell quaternion QGpn and Pell-Lucas QGqn, where components QGqn are numbers pn qn, respectively. Firstly, we obtain recurrence relations Binet formulas for QGqn. We use prove Cassini?s identity these quaternions. Furthermore, give some basic identities such as summation formulas, terms with negative indices generating functions complex

   In This paper, the effect of size on melting temperature of metallic nanoparticles (Au, Pb and Bi) is theoretically simulated and explained. In this regard, the cause of difference in various experimental data is introduced, which is the difference between nanoparticles’ grain Gaussian distribution. This volume-depended model with the help of the Gaussian distribution can descri...