Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a new family of circular distributions that can be skewed more significantly than that of existing models. It is shown that a subfamily of the proposed distributions is identifiable with respect to parameters and all distributions in the subfamily have explicit trigonometric moments and a simple random number generation algorithm. The maximum likelihood estimation for model parameters is considered and its finite sample performances are investigated by numerical simulations. Some real data applications are illustrated for practical purposes.

翻译：正弦偏斜圆分布具有可辨识性、易计算的三角矩以及简单的随机数生成算法，但已知其非对称程度相对较低。本研究提出了一类比现有模型具有更显著偏斜特性的新型圆分布族。研究表明，该分布族的一个子族在参数层面具有可辨识性，且该子族中所有分布均具有显式三角矩和简单的随机数生成算法。本文考虑模型参数的极大似然估计，并通过数值模拟考察其有限样本性能。为满足实际应用需求，本文还展示了若干真实数据应用案例。