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Circular data are measured in angles or directions. In many cases of sampling, instead of a random sample, we deal with a weighted model. In such sampling, observations are provided throughout with a positive function, weight function. This article deals with weight distributions in circular data. According to von Mises distrinution is the most widely used distribution for modeling circular data, maximum likelihood estimation of parameters in weighted von Mises distributions is investigated. In a simulation study, different weights are compared in the Van Mises circular distribution.