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In this paper we developed a statistical model for circular data with noises. In this case, model fitting by single circular model has a lack-of-fit problem. To overcome this problem, we consider some mixture models that include circular uniform distribution and apply an EM algorithm to estimate the parameters. Both von Mises and Wrapped skew normal distributions are considered in this paper. Simulation studies are executed to assess the suggested EM algorithms. Finally, we applied thedoi:10.5351/kjas.2012.25.4.651 fatcat:qxhsdlr45rbppnt3mv7bkpvake