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A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
The last decade of research on elliptical galaxies has produced a wealth of new information concerning both their detailed structure and their global scaling relations. We review the old and new results about isophote shapes and…
We estimate the distribution of intrinsic shapes of the APM galaxy clusters from their corresponding distribution of projected shapes. We smooth the discrete galaxy distribution and define the cluster shape by fitting the best ellipse to…
We analyse the joint distribution of dust attenuation and projected axis ratios, together with galaxy size and surface brightness profile information, to infer lessons on the dust content and star/dust geometry within star-forming galaxies…
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…
To understand how well galaxies, gas and intracluster stars trace dark matter in and around galaxy clusters, we use the IllustrisTNG cosmological hydrodynamical simulation and compare the spatial distribution of dark matter with those of…
Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order…
High-resolution numerical simulations of galaxy mergers are analysed. The global structure and isophotal shapes of the merger remnants are in good agreement with the observations. Whereas equal-mass mergers lead to anisotropic, boxy…
This work finds the non isotropic noncentral elliptical shape distributions via SVD decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape…
We have reanalyzed a data set of 99 low redshift ($ z < 0.1 $) Abell clusters and determined their shapes. For this, three different measures are used. We use Monte-Carlo simulations to investigate the errors in the methods. The corrected…
The distribution of the spin directions of galaxies has been a question in the past decade, with numerous Earth-based and space-based experiments showing that the distribution is not necessarily random. These experiments were based on…
The non isotropic and non central elliptical shape distributions via the Le and Kendall SVD decomposition approach are derived in this paper in the context of invariant polynomials and zonal polynomials. The so termed cone and disk…
The discrete unitary (reversible) analogues of the continuous (irreversible) tent maps are numerically investigated, in particular, the lengths probability distribution of their periodic orbits. It is found that its density can be well…
We consider finite point subsets (distributions) in compact metric spaces. Non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given in the case of general…
Wide binary stars are important for testing alternative models of gravitation in the weak-field regime and understanding the statistical outcomes of dynamical interactions in the general Galactic field. The Gaia mission's collection of…
The notion of $L^p$-distributions is introduced on Riemannian symmetric spaces of noncompact type and their main properties are established. We use a geometric description for the topology of the space of test functions in terms of the…
We develop a new method which measures the projected density distribution w_p(r_p)n of photometric galaxies surrounding a set of spectroscopically-identified galaxies, and simultaneously the projected correlation function w_p(r_p) between…
Recently the termed \emph{multimatrix variate distributions} were proposed in \citet{dgcl:24a} as an alternative for univariate and vector variate copulas. The distributions are based on sample probabilistic dependent elliptically countered…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…