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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 consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…

We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at large…

In recent work, robust mixture modelling approaches using skewed distributions have been explored to accommodate asymmetric data. We introduce parsimony by developing skew-t and skew-normal analogues of the popular GPCM family that employ…

Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the…

In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density,…

Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the…

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…

Background and objective. Circular statistics and Rayleigh tests are important tools for analyzing the occurrence of cyclic events. However, current methods fail in the presence of measurement bias, such as incomplete or otherwise…

A large class of modern probabilistic learning systems assumes symmetric distributions, however, real-world data tend to obey skewed distributions and are thus not always adequately modelled through symmetric distributions. To address this…

Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…

Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on…

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…

In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment…

In this paper, we propose a modification to the density approach to Stein's method for intervals for the unit circle $\mathbb{S}^1$ which is motivated by the differing geometry of $\mathbb{S}^1$ to Euclidean space. We provide an upper bound…

We introduce a new multivariate circular linear distribution suitable for modeling direction and speed in (multiple) animal movement data. To properly account for specific data features, such as heterogeneity and time dependence, a hidden…

We give two new simple characterizations of the Cauchy distribution by using the M\"obius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…