Abstract
Angles and directions are used to measure circular data. To investigate the properties of these data some new statistical tools are required. In the investigation of circular statistics, the observations may enter the sample only with probability proportional to a weighted function rather than randomly. In this paper, by identifying some weight functions in circular data we introduce weighted circular distributions and inferential methods. The topic of maximum likelihood estimation and hypothesis tests for weighted circular distributions are discussed. The performance of weighted circular distributions has been carried out with extensive simulations and the implementation of soil data.
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