Related papers: Circular and Spherical Projected Cauchy Distributi…

We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…

Multivariate circular observations, i.e. points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this…

In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that,…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

The von Mises-Fisher (vMF) distribution has long been a mainstay for inference with data on the unit hypersphere in directional statistics. The performance of statistical inference based on the vMF distribution, however, may suffer when…

Analysis of three-way data is becoming ever more prevalent in the literature, especially in the area of clustering and classification. Real data, including real three-way data, are often contaminated by potential outlying observations.…

This chapter presents a short overview of real elliptically symmetric (RES) distributions, complemented by circular complex elliptically symmetric (C-CES) and noncircular CES (NC-CES) distributions as complex representations of RES…

Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…

Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single…

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…

We develop two novel approaches for constructing skewed and bimodal flexible distributions that can effectively generalize classical symmetric distributions. We illustrate the application of introduced techniques by extending normal,…

We develop a Markov process viewpoint for discrete circular distributions motivated by directional-statistics settings where angles are observed on a finite grid and evolve over time. On the $m$-point discrete circle, the cycle graph, we…

This paper deals with the Elliptical Wishart and Inverse Elliptical Wishart distributions, which play a major role when handling covariance matrices. Similarly to multivariate elliptical distributions, these form a large family of…

We introduce the beta generalized normal distribution which is obtained by compounding the beta and generalized normal [Nadarajah, S., A generalized normal distribution, \emph{Journal of Applied Statistics}. 32, 685--694, 2005]…

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…

In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…

Cylindrical data frequently arise across various scientific disciplines, including meteorology (e.g., wind direction and speed), oceanography (e.g., marine current direction and speed or wave heights), ecology (e.g., telemetry), and…

In this paper we introduce new distributions which are solutions of higher-order Laplace equations. It is proved that their densities can be obtained by folding and symmetrizing Cauchy distributions. Another class of probability laws…

The objective of this work is to propose a new algorithm to fit a sphere on a noisy 3D point cloud distributed around a complete or a truncated sphere. More precisely, we introduce a projected Robbins-Monro algorithm and its averaged…