Related papers: Multivariate generalized Pareto distributions: par…
In this paper we delve into some important properties of probability distributions of the power type in order to provide some answers to questions recently raised in the literature. More precisely, we focus on the properties of maximizers…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…
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.…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
In the present work, we show how the generalized Cram\'er-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on $\mathbb{R}^{n}$, and to a wider…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
The crossing properties of the matrix elements of non-local operators, parameterized by Generalized Parton Distribution, are considered. They are especially simple in terms of the Double Distributions which are common for the various…
This article is written for pedagogical purposes aiming at practitioners trying to estimate the finite support of continuous probability distributions, i.e., the minimum and the maximum of a distribution defined on a finite domain.…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
Pareto distributions are widely used models in economics, finance and actuarial sciences. As a result, a number of goodness-of-fit tests have been proposed for these distributions in the literature. We provide an overview of the existing…
We consider goodness-of-fit methods for multivariate symmetric and asymmetric stable Paretian random vectors in arbitrary dimension. The methods are based on the empirical characteristic function and are implemented both in the i.i.d.…
This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…