A comparative analysis of uniformity tests in circular statistics
Ruiz Mora, Armando Marcial
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In the context of circular statistics, data may not behave uniformly around the circle, exhibiting a preferred direction, thus the need to find appropriate methods to detect departures from a uniform distribution. First, we discuss some uniformity tests for circular data. Then, a likelihood ratio test (LRT) is proposed using standard statistical theory. The cardioid distribution seems particularly adequate as an alternative hypothesis for the LRT when data show a smooth transition in a unimodal preferred direction. Second, when the data are not uniformly distributed, we apply different circular regression methods to devise the patterns of dependence on some independent variables. When the distributional assumptions for parametric regression analysis are violated, a bootstrap method is proposed to test the regression coefficients. Finally, we have applied the uniformity tests and the circular regression methods to analyze wind directional data. Numerical results are summarized in tables for comparison purposes. We observe consistent results that the wind direction is not uniformly distributed via the uniformity tests. For the regression methods, we notice that wind speed is not significant to predict direction while the pattern of wind direction depends on the circular variable time of day.