Related papers: Mixture representations of noncentral distribution…
We investigate existence and properties of discrete mixture representations $P_\theta =\sum_{i\in E} w_\theta(i) \, Q_i$ for a given family $P_\theta$, $\theta\in\Theta$, of probability measures. The noncentral chi-squared distributions…
We show that the distribution of the scalar Schur complement in a noncentral Wishart matrix is a mixture of central chi-square distributions with different degrees of freedom. For the case of a rank-1 noncentrality matrix, the weights 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…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
The cumulative distribution function of the non-central chi-square distribution $\chi_\nu'^2(\lambda),\, \nu\in\mathbb{R}^+$ possesses an integral representation in terms of a generalized Marcum $Q$-function. Regarding some already known…
Bayesian Poisson probability distributions for the average n can be analytically converted into equivalent chi-squared distributions. These can then be combined with other Gaussian or Bayesian Poisson distributions to make a total…
Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…
A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
Two approaches are suggested to the definition of asymmetric generalized Weibull distribution. These approaches are based on the representation of the two-sided Weibull distributions as variance-mean normal mixtures or more general…
By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
The Wishart probability distribution on symmetricmatrices has been initially defined by mean of the multivariateGaussian distribution as an of the chi-square distribution. A moregeneral definition is given using results for harmonic…
We consider in this paper the semiparametric mixture of two distributions equal up to a shift parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. In…
We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises--Fisher, the Watson and the angular Gaussian families. In addition to several special results we…