This paper takes a probabilistic approach to validate novel empirical models and the directional distributional similarities of nearby earthquake counts related to a typical volcano with its eruption duration. Considering the datasets on volcanic eruptions and earthquakes, focusing mainly on earthquakes within a 100-kilometer radius and within a three-year time frame of the volcano eruption. An empirical probabilistic models for the same; statistical model validation tests favor the proposed models is proposed. In addition, a novel directional statistical approach to characterize the interconnection and distributional similarities of volcanic eruptions and earthquakes near volcanoes, utilizing the directional nature of the datasets. The project and partition the volcanic eruption and earthquake data to assess its directional distribution is shown. The analysis demonstrated that the data adhered to a Von Mises distribution and unsupervised equal partition revealed for both datasets, highlighting the interconnected nature of volcanic eruptions and earthquakes. Also, Von Mises-Fisher distribution fit test is applied to this work; the analysis produced partition results that closely aligned with the partitions obtained through the 2D projection. This congruence emphasizes the robustness of the findings in a spherical context. the proposed empirical models and conclusions on distributional similarities may provide insights into the underlying mechanisms connecting these geological phenomena. [ABSTRACT FROM AUTHOR]

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