Related papers: Stochastic dominance for linear combinations of in…
In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified…
We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
In this paper we develop a new tool for the comparison of paired data based on a new criterion of stochastic dominance that takes into account the dependence structure of the random variables under comparison. This new procedure provides a…
Stable distributions are of fundamental importance in probability theory, yet their absolute continuity makes them unsuitable for modeling count data. A discrete analog of strict stability has been previously proposed by replacing scaling…
We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…
We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This result is complemented by proving analogous statements for…
Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying…
We provide conditions for the stochastic dominance comparisons of a risk $X$ and an associated risk $X+Z$, where $Z$ represents the uncertainty due to the environment and where $X$ and $Z$ can be dependent. The comparisons depend on both…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…