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This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…
The non isotropic noncentral elliptical shape distributions via pseudo-Wishart distribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assumption is replaced by assuming a…
It is now well established that galaxies are biased tracers of the distribution of matter, although it is still not known what form this bias takes. In local bias models the propensity for a galaxy to form at a point depends only on the…
In this paper, we study the spherical cardioid distribution, a higher-dimensional and higher-order generalization of the circular cardioid distribution. This distribution is rotationally symmetric and generates unimodal, multimodal, axial,…
Cosmic shear estimation is an essential scientific goal for large galaxy surveys. It refers to the coherent distortion of distant galaxy images due to weak gravitational lensing along the line of sight. It can be used as a tracer of the…
Model--based clustering for directional data data has attracted a lot of interest, but most methods utilize rotationally symmetric distributions. This paper suggests the use of elliptically symmetric distributions, namely the elliptically…
Using recent dust continuum data, we generate the intrinsic ellipticity distribution of dense, starless molecular cloud cores. Under the hypothesis that the cores are all either oblate or prolate randomly-oriented spheroids, we show that a…
There are observational and theoretical indications that both the visible (stars) and the dark matter density distributions in elliptical galaxies increase significantly up to the galactic center. I present here some analytical results…
A solid sphere is considered, with a uniformly distributed infinity of points. Two points being pseudorandomly chosen, the analytical probability density that their separation have a given value is computed, for three types of the…
Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then…
The mass distributions of dense cores in star-forming regions are measured to have a shape similar to the initial mass function of stars. This has been generally interpreted to mean that the constituent cores will form individual stars or…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are…
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
A generalisation of the Charnes-Cooper chance-constrained approach is proposed in the setting of the family of elliptically contoured distributions. The new relaxed stochastic linear programming is notably invariant under the entire class…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…