Related papers: Characterizations of the Cauchy distribution assoc…
In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…
We describe Rudin-Keisler preorders and distribution functions of numbers of limit models for quite o-minimal Ehrenfeucht theories. Decomposition formulas for these distributions are found.
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…
We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new…
Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the…
A quasi-infinitely divisible distribution on $\mathbb{R}$ is a probability distribution whose characteristic function allows a L\'evy-Khintchine type representation with a "signed L\'evy measure", rather than a L\'evy measure.…
It is well known that the Laplace-Stieltjes transform of a nonnegative random variable (or random vector) uniquely determines its distribution function. We extend this uniqueness theorem by using the Muntz-Szasz Theorem and the identity for…
The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the…
The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing…
When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…
Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with…
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…
An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. The new structures are based on a generalization of the concept of symmetry of a distribution of vector fields, inspired in the…
\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…
Using the properties of random M\"{o}bius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the…
Results are presented from calculations carried out in the discrete QCD model, concerning multiplicity distributions in rapidity intervals and fluctuations.
Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte…
The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…