Related papers: On the Conditional Distribution of the Multivariat…
We propose a flexible family of distributions, generalized $t$-distributions, on the cylinder which is obtained as a conditional distribution of a trivariate $t$ distribution. The new distribution has unimodality or bimodality, symmetry or…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…
Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, a new generalization of…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
The textual, big-data literature misses Bentley, OBrien, & Brocks (Bentley et als) message on distributions; it largely examines the first-order effects of how a single, signature distribution can predict population behaviour, neglecting…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting…
The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…
With the help of the methods developed in our previous article [Schmitz, to appear in "Annales de l'I.H.P. Prob. & Stat.], we highlight condition (T) as a source of new examples of 'ballistic' diffusions in a random environment when d>1…
In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
For the directed edge preferential attachment network growth model studied by Bollobas et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails.…
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…