Related papers: Tukey g-and-h neural network regression for non-Ga…

We introduce a new family of multivariate distributions by taking the component-wise Tukey-h transformation of a random vector following a skew-normal distribution. The proposed distribution is named the skew-normal-Tukey-h distribution and…

The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness…

When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time…

Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to…

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities…

The presence of non-Gaussian tails is a prevalent characteristic in many financial modeling scenarios, necessitating the use of complex non-Gaussian distributions such as the generalized beta of the second kind (GB2) and the skewed…

Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…

Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction…

Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also…

With the progress of information technology, large amounts of asymmetric, leptokurtic and heavy-tailed data are arising in various fields, such as finance, engineering, genetics and medicine. It is very challenging to model those kinds of…

The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…

We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework,…

Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…

The velocity distributions of stellar tracers in general exhibit weak non-Gaussianity encoding information on the orbital composition of a galaxy and the underlying potential. The standard solution for measuring non-Gaussianity involves…

Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian…