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In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the
direction of flight of a bird or the orientation of an animal. A series of such observations is called ”directional
data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of
a unit circle centered at the origin or as unit vectors connecting the origin to these points. Because of this circular
representation, such observations are also called circular data. In this paper, circular data will be introduced at first
and then it is explained how to calculate the mean direction, dispersion and higher moments. The solutions to many
directional data problems are often not obtainable in simple closed analytical forms. Therefore, computer softwares
is essential to use these methods. At the end of this paper, the CircStat’s package has been used to analyze data sets
in R and Matlab softwares.

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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.