The Quarter Von Mises Distribution

Oregon Convention Center 

The world today increasingly relies on data science and statistics for analyzing diverse directional data, such as text data, health studies, image processing, wireless sensor networks, environmental monitoring, robotics, geology and materials science. In numerous instances, data exhibit positive orientation and necessitates probability distributions that are confined to positive regions, such as the positive quarter of the unit circle. This article addresses this need by introducing a novelty transformation of the von Mises distribution specifically designed for the positive quarter of the unit circle, filling a current gap in available distributions. The newly proposed distribution, referred to as the Quarter von Mises Distribution, has been thoroughly investigated in this work, including characterizing the distribution through moments and developing its main properties. Additionally, methods for estimating the distribution parameters using maximum likelihood estimation are presented, along with a hypothesis testing approach using the likelihood ratio test. Furthermore, practical data applications are demonstrated to showcase the effectiveness of these methods. Overall, this work

Von Mises distribution


circular statistics

directional statistics


positive quarter


unit circle 

Section on Statistical Computing