This paper investigates the directional distribution of extraterrestrial objects (meteors, fireballs) impacting Earth’s surface and forming craters. It also introduces a novel directional statistical mixture model to analyze their falls, validated through rigorous testing. First, we address whether these falls follow non-uniform directional patterns by explicitly employing directional statistical tools for analysing such data. Using projection techniques for longitude and latitude and more importantly, a general spherical statistical approach, we statistically investigate the suitability of the von Mises distribution and its spherical version, the von Mises–Fisher distribution, (a maximum entropy distribution for directional data). Moreover, leveraging extensive data sets encompassing meteor falls, fireball showers, and craters, we propose and validate a novel mixture von Mises–Fisher model for comprehensively analysing extraterrestrial object falls. Our study reveals distinct statistical characteristics across data sets: fireball falls exhibit non-uniformity, while meteor craters suggest a potential for both uniform and von Mises distributions with a preference for the latter after further refinement. Meteor landings deviate from a single-directional maximum entropic distribution; we demonstrate the effectiveness of an optimal 13-component mixture von Mises–Fisher distribution for accurate modelling. Similar analyses resulted in 3- and 6-component partitions for fireball and crater data sets. This research presents valuable insights into the spatial patterns and directional statistical distribution models governing extraterrestrial objects’ fall on Earth, useful for various future works.

Studying meteoroid impact patterns on planetary surfaces is critical for understanding surface dynamics and selecting safe landing sites. Mercury, one of the least explored rocky planets, presents unique challenges due to its extreme temperatures and the angular nature of its surface data. Traditional linear statistical methods are often inadequate for analyzing such directional data. This study introduces a novel approach using directional data analysis techniques to interpret the cyclical nature of meteoroid impact locations on Mercury. We employed Watson’s test, Bayesian Information Criterion scores, and a mixture of von Mises–Fisher distributions to model the distribution of impact craters and solar elevations on Mercury’s surface. Our findings indicate that while location parameters adhere to the von Mises distribution, solar elevations do not exhibit directional distribution characteristics. Additionally, by filtering datasets based on temperature thresholds and crater diameters, we pinpointed areas with a high probability of providing suitable landing surfaces. These insights enhance our understanding of the surface conditions on Mercury and provide valuable groundwork for future exploration missions.

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.

The study encapsulates the investigation into the spherical distributional characteristics of parameters relevant to Gamma-Ray Bursts (GRBs), mainly focusing on their Galactic coordinates. The study utilized a mixture of von Mises Fisher spherical distributions to model the spatial distribution of GRBs in both BATSE and FERMI catalogs. Optimal numbers of mixture components were determined for different subsets of GRBs, including Long and Short GRBs. For the BATSE catalog, it turns out that a mixture of two spherical distributions provides a good fit for the whole data set and long and short GRBs. On the other hand, for the FERMI catalog, it turns out that a mixture of three spherical distributions provides a good fit for the whole data set, and a mixture of four distributions is adequate for both long and short GRBs. Additionally, an assessment was made to determine if the location parameter of GRBs follows any spherical distribution. Our flexible directional statistical modeling framework reveals that GRBs exhibit a non-uniform distribution on the celestial sphere, as evidenced by rejecting the null hypothesis of uniform distribution on a sphere using the Watson test. Our analysis statistically inquires the long-held assumption of their isotropic spread, especially in 2D projected spatial distributions of GRBs, suggesting that these cosmic events might not be uniformly scattered across the celestial sphere. The observed clumping of GRBs hints at the underlying cosmic scaffolding—the large-scale distribution of matter and star formation. Our results statistically asserts the explanation that the intrinsic GRB formation rate is typically tied to cosmic star formation rates with a delay time distribution, leading to a non-uniform rate as a function of redshift, demanding more nuanced calculations. However, this finding needs to consider potential biases introduced by the Milky Way’s obscuration and our heliocentric perspective.

Globalization and the rise of social media have fundamentally reshaped how individuals construct their identities. This paper explores this phenomenon through an interdisciplinary lens, weaving together philosophical and anthropological perspectives. Philosophical frameworks of existentialism and phenomenology illuminate how algorithms shape lived experiences and self-understandings. Anthropological analysis examines how social media platforms foster virtual communities, impacting cultural norms and individual identities. The paper examines how pre-existing cultural backgrounds and social structures influence the impact of algorithmic culture on the self in a globalized world.