Lévy copulas are the most general concept to capture jump dependence in multivariate Lévy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Lévy copulas, is to find flexible but still...

A new class of copulas referred to as “Sibuya copulas” is introduced and its properties are investigated. Members of this class are of a functional form which was first investigated in the work of M. Sibuya. The construction of Sibuya copulas is based on an increasing stochastic process...

We study the dependence structure of bivariate order statistics from bivariate distributions, and prove that if the underlying bivariate distribution H is positive quadrant dependent (PQD) then so is each pair of bivariate order statistics. As an application, we show that if H is PQD, the...

Let Xt=∑j=0∞cjεt−j be a moving average process with GARCH (1, 1) innovations {εt}. In this paper, the asymptotic behavior of the quadratic form Qn=∑j=1n∑s=1nb(t−s)XtXs is derived when the innovation {εt} is a long-memory and heavy-tailed process with tail index α, where {b(i)} is...

We derive formulae for the higher order tail moments of the lower truncated multivariate standard normal (MVSN), Student’s t, lognormal and a finite-mixture of multivariate normal distributions (FMVN). For the MVSN we propose a recursive formula for moments of arbitrary order as a...

Homogeneous distributions on R+d and on R¯+d∖︀{∞¯d} are shown to be Bauer simplices when normalized. This is used to provide spectral representations for the classical power mean values Mt(x) which turn out to be unique mixtures of the functions x⟼mini≤d(aixi) for t≤1 (with some...

What is the distribution of the product of given powers of independent uniform (0, 1) random variables? Is this distribution useful? Is this distribution commonly used in some contexts? Is this distribution somehow related to the distribution of the product of other random variables? Are there...

This article defines a meaningful concept of elliptical location quantile with the aid of quantile regression, discusses its basic properties, and suggests its extension to a general regression framework through a locally constant nonparametric approach.

A class of models is considered to describe the data to be collected using a design of experiment. One model within the class will possibly describe the data more adequately than the others which will be the “true model” but we do not know its identification. In the pioneering work of...

Consider a stationary Gaussian random field on Rd with spectral density f(λ) that satisfies f(λ)∼c|λ|−θ as |λ|→∞. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data...