Related papers: Probabilities in multimatrix variate distributions…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
We study two different methods for inferring the parameters of a spheroid distribution from planar sections of a stationary spatial system of spheroids: one method first unfolds non-parametrically the joint size-shape-orientation…
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…
The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$…
The univariate Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this article, we define a skewed version of the Birnbaum-Saunders…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…
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…
We introduced a generalized Wishart distribution, namely, the Kotz-Wishart distribution. Several existing results based on the normality assumption have been extended. Inspired by the particular form of the pdf of the Kotz-Wishart matrix,…
The famous \emph{circular law} asserts that if $M_n$ is an $n \times n$ matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution (ESD) of the normalized matrix $\frac{1}{\sqrt{n}} M_n$…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…
In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random…
The class of $\alpha$-stable distributions with a wide range of applications in economics, telecommunications, biology, applied, and theoretical physics. This is due to the fact that it possesses both the skewness and heavy tails. Since…
In this paper, three different proofs to a result of Wang, Peng and Yang (2013) which related to the joint mixability of elliptical distributions with the same characteristic generator are present. Moreover, we generalize this result to any…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
Given a variety over $\mathbb{Q}$, we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…