A Bayesian estimation is considered for unknown parameters of a unimodal skew circular distribution on the circle, where the underlying distribution has mode and anti-mode preserving properties. This distribution is obtained by using a transformation of the inverse monotone function, and the shape of the resulting density can be flat-topped or sharply peaked at its mode. With regard to Bayes estimates (BEs), the boundary-avoiding priors are assumed so that the skewness and peakedness parameters of the distribution do not lie on the boundary of the parameter space. In addition to the BEs, maximum likelihood estimations (MLEs) are conducted to compare the performances in small samples, and found that the BEs are more robust than the method of maximum likelihood. As the pairs of parameters between location and skewness and between concentration and peakedness are independent of each other, approximate BEs using Lindley’s methods become rather simple. Monte Carlo simulations are performed to compare the accuracy of the BE and MLE, and some circular datasets are analyzed for illustrative purposes.

贝叶斯估计被考虑用于圆上单峰斜圆分布的未知参数，其中基础分布具有模态和反模态保持特性。该分布是通过使用反单调函数的变换获得的，并且所得密度的形状在其众数处可以是平顶的或尖峰的。对于贝叶斯估计(BE)，假设边界避免先验，以便分布的偏度和峰值参数不会位于参数空间的边界上。除了 BE 之外，最大似然估计（MLE）用于比较小样本中的性能，发现 BE 比最大似然方法更稳健。由于位置和偏度之间以及浓度和峰值之间的参数对彼此独立，因此使用 Lindley 方法的近似 BE 变得相当简单。进行蒙特卡罗模拟以比较 BE 和MLE 的准确性，并分析一些圆形数据集以进行说明。