Related papers: Characterizations of the Cauchy distribution assoc…
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 introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped…
We present some properties of a Cauchy family of distributions on the sphere, which is a spherical extension of the wrapped Cauchy family on the circle. The spherical Cauchy family is closed under the M\"obius transformation on the sphere…
The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…
It is shown that a family of distributions on the complex space is characterized as the only family such that the orbit of one distribution under a certain group of transformations on the complex space is the same as that under the group of…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
Identifiability of statistical models is a fundamental and essential condition that is required to prove the consistency of maximum likelihood estimators. The identifiability of the skew families of distributions on the circle and cylinder…
A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either…
In this paper, we discuss some special properties of operator- valued semicircular random variables including representation of the Cauchy transform of a compactly supported probability measure in terms of their operator-valued Cauchy…
A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous)…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
We report a closed-form expression for the Kullback-Leibler divergence between Cauchy distributions which involves the calculation of a novel definite integral. The formula shows that the Kullback-Leibler divergence between Cauchy densities…
In this paper we provide a systematic exposition of basic properties of integrated distribution and quantile functions. We define these transforms in such a way that they characterize any probability distribution on the real line and are…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
A new characterization of the multivariate so-called "quasi-Gaussian distribution" (the authors dared to coin a new term) by means of independence their Cartesian and polar coordinates proposed. The authors try to show that these…
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series…
We present several recent results concerning Cauchy and event horizons. In the first part of the paper we review the differentiablity properties of the Cauchy and the event horizons. In the second part we discuss compact Cauchy horizons and…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…