2,141 research outputs found
Joint Mixability of Elliptical Distributions and Related Families
In this paper, we further develop the theory of complete mixability and joint
mixability for some distribution families. We generalize a result of
R\"uschendorf and Uckelmann (2002) related to complete mixability of continuous
distribution function having a symmetric and unimodal density. Two different
proofs to a result of Wang and Wang (2016) which related to the joint
mixability of elliptical distributions with the same characteristic generator
are present. We solve the Open Problem 7 in Wang (2015) by constructing a
bimodal-symmetric distribution. The joint mixability of slash-elliptical
distributions and skew-elliptical distributions is studied and the extension to
multivariate distributions is also investigated.Comment: 15page
A unified treatment of characteristic functions of symmetric multivariate and related distributions
The purpose of the present paper is to give unified expressions to the
characteristic functions of all elliptical and related distributions. Those
distributions including the multivariate elliptical symmetric distributions and
some asymmetric distributions such as skew-elliptical distributions and their
location-scale mixtures. In particular, we get simple closed form of
characteristic functions for important cases such as the multivariate
Student-, Cauchy, logistic, Laplace, symmetric stable. The expressions of
characteristic functions involve Bessel type functions or generalized
hypergeometric series.Comment: 17 page
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
On the Independence Jeffreys prior for skew--symmetric models with applications
We study the Jeffreys prior of the skewness parameter of a general class of
scalar skew--symmetric models. It is shown that this prior is symmetric about
0, proper, and with tails under mild regularity conditions.
We also calculate the independence Jeffreys prior for the case with unknown
location and scale parameters. Sufficient conditions for the existence of the
corresponding posterior distribution are investigated for the case when the
sampling model belongs to the family of skew--symmetric scale mixtures of
normal distributions. The usefulness of these results is illustrated using the
skew--logistic model and two applications with real data
Hessian and increasing-Hessian orderings of multivariate skew-elliptical random vectors
In this work, we establish some stochastic comparison results for
multivariate skew-elliptical random vectors. These multivariate stochastic
comparisons involve Hessian and increasing-Hessian orderings as well as many of
their special cases. Necessary and/or sufficient conditions of the orderings
are provided simply based on a comparison of the underlying model parameters.Comment: 2
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