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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. [ABSTRACT FROM AUTHOR]

Galaxies are one of the most interesting and complex astronomical objects statistically due to their continuous diversification caused mainly due to incidents such as accretion, action, or mergers. Multivariate studies are one of the most useful tools to analyze these type of data and to understand various components of them. We study a sample of the local universe of Orlando 509 galaxies, imputed with a Predictive Mean Matching (PMM) multiple imputation algorithm, with the aim of classifying the galaxies into distinct clusters through k-medoids and k-mean algorithms and, in turn, performing a heuristic evaluation of the two partitioning algorithms through the percentage of misclassification observed. From the clustering algorithms, it was observed that there were four distinct clusters of the galaxies with misclassification of about 1.96 % . Also, comparing the percentage of misclassification heuristically k-means is a superior algorithm to k-medoids under fixed optimal sizes when the said category of galaxy datasets is concerned. By considering that galaxies are continuously evolving complex objects and using appropriate statistical tools, we are able to derive an explanatory classification of galaxies, based on the physical diverse properties of galaxies, and also establish a better method of partitioning when working on the galaxies. [ABSTRACT FROM AUTHOR]

Quasars are astronomical star-like objects having a large ultraviolet flux of radiation accompanied by generally broad emission lines and absorption lines in some cases found at large redshift. The used data is extracted from the Veron Cetti Catalogue of AGN and Quasar. The objective of this work is to partition the quasar based on their spectral properties using multivariate techniques and classify them with respect to the obtained clusters. Performing the K-means partitioning method, two robust clusters were obtained with cluster sizes 39,581 and 129,377. The percentage of misclassification observed based on the obtained clusters considering a multivariate classification technique and machine learning classification algorithm, i.e., linear discriminant analysis and XG-Boost, respectively. The linear discriminant analysis and XG-Boost evaluated a misclassification of around 0.84 and 0.15%, respectively. Additionally, a heuristic literature-based categorization subject to redshift yielded an accuracy of around 96%. This gives us cross-validating arguments about the astronomical data, that machine learning algorithms might perform on par with conventional multivariate techniques, if not better. [ABSTRACT FROM AUTHOR]