Related papers: Statistical Inference for Mixture of Cauchy Distri…
The Cauchy-Rayleigh (CR) distribution has been successfully used to describe asymmetric and heavy-tail events from radar imagery. Employing such model to describe lifetime data may then seem attractive, but some drawbacks arise: its…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new…
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is…
We propose a new formulation of the probability distribution function of wind driven water surface slope with an $\alpha$-stable distribution probability. The mathematical formulation of the probability distribution function is given under…
This is an extended version of the paper Lee and McLachlan (2014b) with simulations and applications added. This paper introduces a finite mixture of canonical fundamental skew t (CFUST) distributions for a model-based approach to…
Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There…
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family,…
In the present study examines the statistical structure of the generated randomized density of the normal distribution and the Cauchy distribution. The study put the allegation that a randomized probability density of the normal…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
The problem of calculating the probability density and distribution function of a strictly stable law is considered at $x\to0$. The expansions of these values into power series were obtained to solve this problem. It was shown that in the…
Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
In the past few years, there have been a number of proposals for generalizing the factor analysis (FA) model and its mixture version (known as mixtures of factor analyzers (MFA)) using non-normal and asymmetric distributions. These models…
Analysis of matrix-variate data is becoming increasingly common in the literature, particularly in the field of clustering and classification. It is well-known that real data, including real matrix-variate data, often exhibit high levels of…
Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace…
We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…
In recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. A parameter-wise co-clustering model, for data modelled via continuous…
The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…