Related papers: New Developments on the Non-Central Chi-Squared an…
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…
We present formulas for the (raw and central) moments and absolute moments of the normal distribution. We note that these results are not new, yet many textbooks miss out on at least some of them. Hence, we believe that it is worthwhile to…
In the present paper new light is shed on the non-central extensions of the Dirichlet distribution. Due to several probabilistic and inferential properties and to the easiness of parameter interpretation, the Dirichlet distribution proves…
The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
The solution of QCD equations for generating functions of multiplicity distributions reveals new peculiar features of cumulant moments oscillating as functions of their rank. This prediction is supported by experimental data on $e^{+}e^{-},…
In this note the use of the zero degree non-central chi squared distribution as predictive distribution for ensemble postprocessing is investigated. It has a point mass at zero by definition, and is thus particularly suited for…
For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for…
With any symmetric distribution $\mu$ on the real line we may associate a parametric family of noncentral distributions as the distributions of $(X+\delta)^2$, $\delta\not=0$, where $X$ is a random variable with distribution $\mu$. The…
The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result…
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…
We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
Models phrased though moment conditions are central to much of modern inference. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the…
This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce, using probabilistic approaches, lower and…
A (p-1)-variate integral representation is given for the cumulative distribution function of the general p-variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known…
Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the…