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This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
This paper introduces the multivariate beta mixture model (MBMM), a new probabilistic model for soft clustering. MBMM adapts to diverse cluster shapes because of the flexible probability density function of the multivariate beta…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
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…
We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…
While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite…
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…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
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…
In this paper, we introduce a new multivariate discrete distribution which called multivariate unification of generalized Apostol type distribution (UGAT). Several prop- erties are studied as, moments, probability generating function and…
When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…
The univariate Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this article, we define a skewed version of the Birnbaum-Saunders…
Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…