Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in...

There has been much work on the approximation of independent or dependent random variables. But we are not aware of any work giving exact results for the approximation of the sum of randomly weighted random variables. In this paper, we derive results for the randomly weighted sum of dependent...

This paper studies random vectors X featuring symmetric distributions in that i) the order of the random variables in X does not affect its distribution, or ii) the distribution of X is symmetric at zero. We derive a number of characterization results for such random vectors, thereby connecting...

We introduce the new F-Riesz distribution to model tail-heterogeneity in fat-tailed covariance matrix observations. In contrast to the typical matrix-valued distributions from the econometric literature, the F-Riesz distribution allows for di↵erent tail behavior across all variables in the...

This paper considers the randomly weighted sums generated by some dependent sub-exponential primary random variables and some arbitrarily dependent random weights. To study the randomly weighted sums with infinitely many terms, we establish a Kesten-type upper bound for their tail probabilities...

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for...