Quarter von Mises distribution

The world today is increasingly relying on data science and statistics to analyze various types of directional data, such as text data, health studies, image processing, wireless sensor networks, environmental monitoring, robotics, and materials science. In many cases, these data exhibit positive orientation and require probability distributions that are confined to positive regions, such as the positive quarter of the unit circle. These facts highlight the main objective of this thesis, which is to propose a new transformation of the von Mises distribution specifically tailored for the positive quarter of the unit circle. Currently, no such distribution exists. The newly introduced distribution, referred to as the Quarter von Mises Distribution, has been thoroughly investigated in this work. The research includes 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 thesis contributes to the field of data science and statistics by providing a novel distribution that can accurately model directional data restricted to the positive quarter of the unit circle.