Inferring the most appropriate distribution (or distributions) to describe observed directional data is important in many applications of circular statistics. In particular, animal movement paths are typically analysed and modelled by considering the distribution of step lengths and turning (or absolute) angles. Here we demonstrate that a single-wrapped Cauchy distribution can appear to fit directional data mixed from two different underlying wrapped normal distributions. We derive mathematical expressions to calculate the parameter space for which this occurs and illustrate the result by analysing an example data set of the movements of African bull elephants (Loxodonta Africana). We conclude that the presence of a wrapped Cauchy distribution in observed directional data can, in certain cases, be explained by data coming from two distinct underlying distributions. We discuss how this may relate to the presence of multiple movement modes within an observed path when analysing animal movement data.

在循环统计的许多应用中，推断最合适的分布（或多个分布）以描述观察到的方向数据非常重要。特别是，通常通过考虑步长和转弯（或绝对）角度的分布来分析和建模动物的运动路径。在这里，我们证明了单层柯西分布似乎可以适应来自两个不同的基础包裹正态分布的方向数据。我们导出数学表达式来计算发生这种情况的参数空间，并通过分析非洲斗牛象（Loxodonta Africana）运动的示例数据集来说明结果。）。我们得出的结论是，在某些情况下，观察到的定向数据中存在包装的柯西分布，可以用来自两个不同基础分布的数据来解释。我们在分析动物运动数据时讨论了这可能与观察路径内多个运动模式的存在有关。