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Several distributions and families of distributions are proposed to model skewed data, think, e.g., of skew-normal and related distributions. Lambert W random variables offer an alternative approach where, instead of constructing a new…

Methodology · Statistics 2023-10-17 Meelis Käärik , Anne Selart , Tuuli Puhkim , Liivika Tee

In this paper, we present an algorithm for the fitting of a location-scale variant of the canonical fundamental skew t (CFUST) distribution, a superclass of the restricted and unrestricted skew t-distributions. In recent years, a few…

Methodology · Statistics 2014-02-03 Sharon X. Lee , Geoffrey J. McLachlan

We consider the extremal properties of the highly flexible univariate extended skew-normal distribution. We derive the well-known Mills' inequalities and Mills' ratio for the extended skew-normal distribution and establish the asymptotic…

Methodology · Statistics 2018-10-01 Boris Beranger , Simone A. Padoan , Yangfan Xu , Scott A. Sisson

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…

Probability · Mathematics 2024-05-14 Robert E. Gaunt , Siqi Li

Recently, expectile-based measures of skewness akin to well-known quantile-based skewness measures have been introduced, and it has been shown that these measures possess quite promising properties (Eberl and Klar, 2021, 2020). However, it…

Statistics Theory · Mathematics 2022-05-18 Andreas Eberl , Bernhard Klar

This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred to as the matrix Fisher distribution is…

Optimization and Control · Mathematics 2020-05-04 Taeyoung Lee

Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely…

solv-int · Physics 2015-06-26 M. Adler , P. J. Forrester , T. Nagao , P. van Moerbeke

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…

Methodology · Statistics 2009-11-13 Adelchi Azzalini , Antonella Capitanio

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…

Machine Learning · Statistics 2024-07-31 Abhranil Das , Wilson S Geisler

We introduce a natural generalization of Maya diagrams -- the space of infinite Fibonacci configurations, which are specified functions on $\mathbb{Z}$ with values $1$ and $0$. Infinite Fibonacci configurations are particularly interesting…

Combinatorics · Mathematics 2024-03-15 Timur Kenzhaev

We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…

Dynamical Systems · Mathematics 2013-01-25 A. Vershik

In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution, focusing our attention on the symmetric weakly stable distribution. As in the case of the classical…

Probability · Mathematics 2008-10-30 W. Jarczyk , J. Misiewicz

Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that…

Computation · Statistics 2007-12-28 Peter Hoff

The weight distribution of an error correcting code is a crucial statistic in determining it's performance. One key tool for relating the weight of a code to that of it's dual is the MacWilliams Identity, first developed for the Hamming…

Information Theory · Computer Science 2023-05-03 Izzy Friedlander , Thanasis Bouganis , Maximilien Gadouleau

In this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chebyshev polynomials of the first kind and the error function. Also, we…

General Mathematics · Mathematics 2025-12-30 Zeraoulia Rafik , Alvaro H Salas , David L Ocampo

Class distribution skews in imbalanced datasets may lead to models with prediction bias towards majority classes, making fair assessment of classifiers a challenging task. Metrics such as Balanced Accuracy are commonly used to evaluate a…

Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…

Probability · Mathematics 2015-09-09 Zhiyi Chi

We introduce a novel matrix-variate extension of the Heckman selection model to accommodate multiple outcomes, providing a flexible and natural generalization of classical selection models for matrix-valued data. By relying on the matrix…

Methodology · Statistics 2026-05-05 Heeju Lim , Carlos A. R. Diniz , Ofer Harel , Victor H. Lachos

We characterize the identified sets of a wide range of stochastic choice models, including random utility, various models of boundedly-rational behavior, and dynamic discrete choice. In each of these settings, we show two distributions over…

Theoretical Economics · Economics 2026-02-24 Peter Caradonna , Christopher Turansick

In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, using which the characteristic function of the product and…

Statistics Theory · Mathematics 2016-11-10 Taras Bodnar , Stepan Mazur , Stanislas Muhinyuza , Nestor Parolya